Everything the germans called a tank destroyer was turretless. The US had a strange fetish with semi-armored "tank destroyers" that featured uncovered turrets and barely adequate armor.
Anyhow, there are two very good reasons for the lack of turrets here:
I've sat in a Hetzer and I will say that things feel real cramped -- there was not a lot of room once they shoe-horned that 75mm gun into that chassis. Would have been very, very exciting to be sitting in there when the MA was fired.
To put some meat on this - the size of gun a turreted tank can mount is determined by the size of the turret ring. This, in turn, is decided by how wide you can make your tank, which is in turn, decided by external factors like the railway loading gauge (the Tiger had to have special tracks fitted to be moved by rail, and the Churchill had to have its radiator louvres removed to fit the smaller British loading gauge.
To fully understand this, bear in mind that the breach will extend a fair way into the turret and that there still needs to be enough space left over for a round to be loaded. Here is a photo of the inside of Valentine with a 2pdr (40mm) road being loaded. And Here is a photo of a crew loading 17pdr rounds into a Sherman Firefly. This photo shows how cramped things were for the loader inside a Firefly. Not much room at the inn!
Early war designs like the M3 Lee and the earlier marks of Churchill had larger guns mounted in the hull and smaller guns in the turret to try and get around this problem.
The advantage of the turretless tank destroyer is that you don't have to worry about turret rings or anything like that. Its just a big old gun inside an enclosed armoured casemate. Although even so, there wasnt much space left over when the 88 was fitted to something as large and as rare as a Jagdpanther as shown here
The added advantages are that:
Manufacturing is simplified. Turret rings are tricky to produce and you dont have to worry about any of the other gubbins involved in producing a workable turret.
You can use the weight saved to slap on some nice thick armour on the frontal glacis, which now extends to the whole front of the vehicle since
The the vehicle now has a lower profile without a turret sat on top of it
you can re-purpose hulls from older, obsolete vehicles to accommodate a large enough gun to be effective on the battlefield (for example the Hetzer was a re-purposed pre-war Czech design).
The obvious disadvantage that you can only fire in a limited arc is offset by tactical ustilisation of the frontal glacis. That is, you use a TD like a an anti-tank artillery piece with better protection and much improved mobility.