For as impassioned of a debate as this is, there have been relatively few facts and numbers put down. So let's go ahead and add some of those.
First up, in 2784 the combined strength of the Great Houses was 984 regiments (FS: 220, CC: 184, DCMS: 230, FWL: 170, LC: 180). That's opposed by the 613 remaining regiments of the SLDF. As far as the SLDF went, however, that strength was more than enough to double the TH garrison while retaining the same force in the single nearest military district to the TH as was there prior to 2765.
On the naval side, things were substantially better for the SLDF. There they were outnumbered only 402 to 478. However, their ships had HPGs and LF batteries. Additionally, we know there are another 67 warships that the SLDF did not take with them but which were reconstructable (as C*, WoB, & FWL did). That would bring them to near parity but with the SLDF having a substantial advantage due to their centralized location and faster speeds.
We lack information for the experience of both sides, but LoT, both books, make clear that there were a lot of veterans who fought for the entire war. That's considerable experience there and far more than anything that the Houses could establish.
But we do have some anecdotal evidence to suggest that the SLDF ground forces would have been even more ferocious. We know the SLDF suffered a 70% loss of strength between 2765 and 2785. However, if you look at the Royal Commands the average loss across all commands there was 45.92%. That's a substantially better rate than that of the regular command (75.90%).
So with the Royals, the people most committed to defending the Terran Hegemony, they are more experienced, better equipped, and more loyal to their home. But can we provide any data that would suggest they would remain loyal? Yes. For starters, none of the eight units who defected prior to the Exodus were Royal units. Additionally, their loyalty to Kerensky was unquestioned. The idea of leaving the IS should have struck people as insane and yet, among the Royal commands, 93.18% joined him. Even among the Royals, 73.68% chose to leave. Its hard to conjure up a situation where people whose loyalty was that fanatical could be convinced to desert the SLDF.
So perhaps this evidence is enough to suggest that the SLDF could hold the TH against one or some of the houses. But all of this just deals with the SLDF. It doesn't suggest how the SLDF could possibly hold against all. Well, the reality there is that they wouldn't need to. As I mentioned at the beginning of this post, the SLDF had plenty of forces to hold the inner third most of each great house as well as strengthen the TH. So if they pulled out, would the Great Houses have remained still? Of course not. The Periphery states would have been undefended. LoT confirms that the LC was more than happy to eat up the RWR in that situation. Would the DC & FS have ignored the OA? Would the CC & FS have ignored the TC? Would the FWL have ignored the MoC? Its hard to believe they would have when their other options would have involved going up against fully armed forces elsewhere.
And on top of that, the outer half of each border, roughly, would no longer have had an SLDF presence. If the LC really wanted to go after the Bolan Thumb, they could have. Or they could pick a fight with the FWL and SLDF. Why would they? The SLDF had plenty of forces to hold the TH and play the houses against each other.
But let's say a Great House did pick a fight against the SLDF. Let's even make it the biggest and baddest with the DCMS. 230 regiments versus the SLDF's 613. The DCMS did not have the means to get every regiment moving, and they certainly wouldn't have stripped the FS and LC borders. Could the DCMS's 84 warships have held off the SLDF's 402(+67)? Its hard to see how.
And these situations are based on the SLDF in 2783, the last year we have been given data prior to the Exodus. Kerensky would have devoted more resources to rebuilding the SLDF and the defenses on each planet. The SLDF would have been stronger. The planets would have been stronger. Relations between the SLDF/TH and the LC, CC, and FS would have been better. With a stronger SLDF I don't see how Barbara Liao or John Davion suddenly get the urge to take it on.