One of common themes in early Imperial Rome, say 1st century AD, is that Rome simply didn't have enough standing legions to do all it wanted/needed to do. If they needed to go on offensive on one border it had to weaken other. Or when threatened on one border it had to shuffle legions from another, thus weakening it. For example conquest and pacification of Britannia required 4 legions, whose absence was felt elsewhere.
So why not raise couple more? Sure, it was expensive but surely exposing border to enemies because there were not enough legions to go around was worse and more expensive in long run? Given that in the Year of IV Emperors usurpers raised their own legions surely Rome itself could do same and sustain them.
The answer is a combination of money and logistics. Augustus set the imperial army at 28 legions (reduced to 25 after the Battle of Teutoberg.) This number gradually increased over time and peaked under Septimius Severus at 33. However, Augustus settled on the number 25 because it was the sufficient amount needed to defend the borders that the Empire could reasonably afford.
Because Rome had stable, natural borders to the south (Sahara) and west (Atlantic), the bulk of the Legions were stationed on the Rhine, Danube, and Syria. The Roman army and allied forces exceeded some 300,000 men, which was by far the largest expense of the imperial budget. Maintaining and paying this professional army was incredible costly. It also meant that many provinces, particularly those in Western Europe, operated at a budgetary deficit. Without the tax revenue from the Eastern provinces, Rome wouldn’t have been able to support such a large army in the west. It also meant that the Emperor had to take a hard look at the viability of a potential province. If it wouldn’t generate enough tax revenue to fully support the legions stationer there, then the Empire needed a very strong reason to try to annex it.
When Augustus became sole ruler of Rome, he stabilized the existing borders and made it policy not to expand. The Legions existed as a defensive weapon, not offensive. The Legions did make war with tribes and kingdoms on the borders, however this was largely to force agreeable peace terms. The seasonal campaigns were not meant to conquer new territory.
Tiberius and Caligula continued Augustus’s policy. The only reason Claudius invaded Britain is because he had no military experience and highly questionable credibility at the time of his rise to power. He needed a military campaign the would impress the Roman people and Britain presented the perfect opportunity. It is worth noting that even after the conquest of Britain, Nero seriously considered abandoning the island because it was considered too expensive to defend. He chose not to, largely because it would have been bad PR. For the next 400 years, the only territories that Rome added were during Trajan’s conquests in the second century CE. All of these except Dacia were immediately abandoned by Hadrian because they would have been too expensive to pacify and maintain. Dacia was found to have many gold and silver mines, so it was worth the effort.
In short, the existing Legions were a defensive measure towards external pressure, not internal. So when there were internal pressures, i.e. civil wars, the Legions were pulled away from their regular duties to meet the more pressing issue. Generals who were trying to win a civil war did not have time to recruit, train, and prepare new legions. (They also might not have the money.) They needed to knock out their rivals as quickly as possible. For example, when Pertinax was murdered by the Praetorian Guard, Septimius Severus took his Pannonian Legions to Rome in a matter of days. Meanwhile, Pescennius Niger, Governor of Syria, took months to approach. In that time, Severus defeated another rival, shored up his position, and was ready for the approaching eastern army.
We also have several examples where newly recruited legions were quickly and easily defeated during civil wars. Julius Caesar’s veteran army made short work of Pompey’s new legions. Several hundred years later, Constantine the Great’s army did the same to Maxentius’s new recruits. The new recruits were not fit for combat, especially against hardened veterans.
TLDR: Rome budgeted the Roman Legions to defend the borders, not for generals winning civil wars. When wars did break out, the urgency of the situation necessitated moving experienced soldiers off the borders to front line to win the war. Raw recruits were no match for veterans in combat and were no substitute for them in the border defenses.