The examples of mass graves for crucified/criminal victims that we have outside the Esquiline gate are not found anywhere in Israel. We know that the Romans executed thousands of Jews, but we don't know what they did with them afterwards - but we suffer an additional problem in that we can't find very many dead people at all in Israel. They obviously died, but the population was disposed of and nobody knows exactly how and where. They didn't do cremations, so burial is most obviously the next choice, but where is a mystery. Ossuaries are definitely used, but there's not enough of them to cover all the dead in Judea (this isn't just a Roman period problem, it's goes back into the Iron Age).

You've mentioned that the Romans left people on crosses for days, but that's not always the case. The Spartacus rebellion left the crucified outside, and Titus crucified Jews in front of Jerusalem in AD70, but the examples of corpse exposure after crucifixion are during times of war and rebellion, not peace time. While it's true that corpse abuse sometimes took place, both Roman, Jewish, and Greek writers expressed their abhorrence about it, and most of those executed by the Romans were afforded burial afterwards and we have plenty of archaeological examples of capital executions being buried. Roman law required the burial of the condemned except in the case of high treason (Digest 48.24.0). Romans leaving Jesus on the cross would also have offended the Jews for no particular reason and both the texts in Mark and in Acts have the Jews taking down the body and burying it. Josephus echoes this:

Jews used to take so much care of the burial of men, that they took down those that were condemned and crucified, and buried them before the going down of the sun Jewish War, 4.317

and Deuteronomic law required the dead to be buried on the same day (Deut 21:22-3) so the fact that Jesus would be buried is pretty much a certainty. The issue is exactly where. The sole example we have a crucified victim anywhere in the Roman empire, is in a tomb in Israel.

There's no requirement that criminals must be buried in a particular place, and the very few examples we have in writing about crucifixions in Judea say nothing about where they would be buried only that they were (Josephus cries to Titus that 3 crucified men were his friends, and they were taken down off their crosses!) There's no 'criminal' burial places in Judea, no mass graves, so it's difficult to tell whether the narrative about Jesus' tomb is impossible, there's nothing to stop Jesus from being buried in another's tomb.

If you want to poke around with some monographs on the subject:

• Chapman, David W., Ancient Jewish and Christian Perceptions of Crucifixion (Grand Rapids, Mich: Baker Academic, 2010)
• Cook, John Granger, Crucifixion in the Mediterranean World, 2014
• Samuelsson, Gunnar, Crucifixion in Antiquity: An Inquiry into the Background and Significance of the New Testament Terminology of Crucifixion (Tübingen: Mohr Siebeck, 2011)

You'll hear a lot about older and earlier claims about crucifixion and what happens (cf Crossan) but the above 3 titles have moved beyond him and his generation and must be taken as the starting point - especially Cook. This is because you cannot take what happens in Rome and extrapolate to Judea -even the format of crucifixion is geographically specific.

Jodi Magness and Rachel Hachlili have some good stuff on burial customs, Byron McCane's Roll back the Stone and Mark D Smith's The Final Days of Jesus have some other good archaeological and sociological points that are well worth reading up on.

There's a decent paper by Cook 2011 on this. It only argues that a burial by JoA is comprehensible to the reader, not that it is absolute history. Cook also finds there are no extant pit burial sites yet identified in Judea - that doesn't mean they didn't exist, but if they did we haven't found them making a pit "burial" less likely.

In my layman view there are three entirely separate narratives to be found in the Bible that attest to there being a burial: 1. Paul (1 Cor 15:4), 2. Luke (Acts 13:29), 3. Mark (Mark 15:42-57, Matt 27:57-61, Luke 23:50-56, John 19:38-42). (Obviously I'm just using the traditional names to refer to the anonymous/unidentified authors of the works of Acts and Mark).

As to how likely it is, I can't really say. It does appear to be an early belief, as Paul most likely learned the 1 Cor 15 Creed from Cephas and James c. 35 AD (see Gal 1:18-19), it seems quite likely because they're the only two Apostles he names specifically as receiving Christophanies (1 Cor 15:5,7). And the Jews would have had to have provided some kind of burial for the criminal and poor, we just don't know exactly what it was at that time. Did they have tombs reserved for criminals? Did they bury them in individual shallow graves outside the city? Did they put them in open pits/mass burial sites? The only thing that seems almost impossible is that they burned/cremated the bodies.

However, here's where the problem with historicity begins. Most critical scholars think that the disciples fled to Galilee when Jesus was crucified, and that's where Cephas (or at least one disciple) had the first Christophany ("virtually certain" according to Lindars 1986). Lindars was a NT scholar who rejected the empty tomb narrative, but believed in a physical resurrection. Lindars notes in his paper though that it's futile to make definitive statements about what the nature of the Christophanies were:

"It seems to me impossible to dogmatize about the nature of these experiences, however. We must leave it open whether the appearance was what one might call 'objective' (Acts9, for what it is worth, implies not), or was a vision confined to the beholder, or was an intellectual illumination in the sense of a flash of realization of a truth." (p. 92).

So, they probably weren't there to witness a burial (however at least one of them was likely there to witness the cry of dereliction before Jesus died). The visions are what triggered off the preaching of the resurrection, not the discovery of an empty tomb. There's no reason to accept the timeline proposed by the Evangelists, it may well have been many months before the first "vision" of Jesus (note that neither Acts 13 nor 1 Cor 15 claim the appearances happened immediately, nor do they make any mention of the crucifixion occurring during Passover for that matter). So what this suggests is that at least Cephas and James believed that Jesus was buried as this is what they tell Paul - but they didn't necessarily have any hard evidence or proof that Jesus was taken down from the cross by the the Jews and buried. Notably, if there was an empty tomb it is never appealed to or attested to by Paul, and no attempt was made to enshrine the site which is what we might expect had such a miracle occurred.

Anyway, I come back to the point that no one was there to actually witness a burial. The women mentioned were disciples that would have left with the others to go to Galilee, and the empty tomb narrative is so unlikely to be based in any historical detail that it removes the would-be witnesses. By the time they came back to Jerusalem (and we don't know when that was as per Lindars "We cannot tell how much time elapsed before Jerusalem became the centre, but it would be a mistake to suppose that everything happened with the speed that is suggested by Luke in the early chapters of Acts."; p. 93) they believed or wanted to believe that Jesus had been buried. But by this time it would have been impossible for anyone to locate the body of Jesus had it been buried in a shallow grave, in a pit, or even in a tomb. Not the disciples, not the Jews that buried him, not the family of Jesus, and not even the Romans would have been able to find the body a year later. And that's IF it was buried at all:

"Even if Pilate actually thought Jesus was guilty of some kind of political disturbance, he could have allowed the burial. But one cannot deny the possibility that, against the evidence of the gospels, Pilate refused to permit any kind of burial for Jesus." (Cook, 2011 p. 204).

I don't think we can say how likely it was because we simply don't know if Pilate allowed crucified criminals to be buried in the first place, or if he did how likely he would be to grant such a request. I would say the specific claim that JoA put him in his family tomb is unlikely, but anything is possible.

There have been a few recent posts about this on /r/AcademicBiblical