I'm not sure if I agree with the assessment of Taylor. That's not to say that your overall characterization is wrong, but some of the political points seem misinterpreted.
Taylor's desire to quickly admit free states from the newly acquired Mexican territory supposedly originated not from any particular views on slavery, but instead from a desire to see proper governments set up in these areas. Taylor, having fought in the Mexican-American War, was quite familiar with how disorganized these areas were and was invested in correcting that as quickly as possible, especially as settlers moved westward and infrastructure would be needed. He believed that debating the legality of slavery in these territories would've stalled the process, potentially for years. Establishing a state, with whatever constitution they proposed, was a legal way to bypass Congress' authority and the political squabbling that would've come with it.
Additionally, Taylor was a Whig and seemingly stuck with many of their principles. Whigs were generally against the use of the veto, so it's unlikely Taylor would've exercised that in any scenario where Congress had reached a compromise. That's basically the exact opposite of what we would expect him to do. Additionally, the Whigs had for decades promoted the idea that a president should only serve one term, so Taylor is unlikely to run again in 1852. Not to mention that he'd be around 68 years old at that time. He had had malaria in 1844 and possibly cholera in 1849, which supposedly sapped much of his strength until 1850 when he he caught cholera (again) and died. I'm sure both he and the Whigs would be conscious of that.
Lastly, the Whigs were already starting to fray around this time. Even if Taylor had been around to lead them, the Northern and Southern branches of the party are already politically diverging. And the economic boom that followed the Mexican-American War is still going to happen, perhaps even more so if Taylor quickly organized states in the west. That may seem like a boon, but in reality it undermined the Whig's messaging on the necessity of a proactive government. Having no official stance on slavery and having no economic messages meant the Whigs had little to organize around, which is why the party fractured in OTL. If southern states attempt some form of secession, I agree with you that Taylor would be quick to quash it and the South would probably see its political power dwindle. I expect in such a scenario that Taylor might lead some sort of unionist party rather than specifically reinvigorate the Whigs. However, all that said, such a scenario would violate the premise of this thread which was to avoid conflict over secession.
Taylor's desire to quickly admit free states from the newly acquired Mexican territory supposedly originated not from any particular views on slavery, but instead from a desire to see proper governments set up in these areas. Taylor, having fought in the Mexican-American War, was quite familiar with how disorganized these areas were and was invested in correcting that as quickly as possible, especially as settlers moved westward and infrastructure would be needed. He believed that debating the legality of slavery in these territories would've stalled the process, potentially for years. Establishing a state, with whatever constitution they proposed, was a legal way to bypass Congress' authority and the political squabbling that would've come with it.
Additionally, Taylor was a Whig and seemingly stuck with many of their principles. Whigs were generally against the use of the veto, so it's unlikely Taylor would've exercised that in any scenario where Congress had reached a compromise. That's basically the exact opposite of what we would expect him to do. Additionally, the Whigs had for decades promoted the idea that a president should only serve one term, so Taylor is unlikely to run again in 1852. Not to mention that he'd be around 68 years old at that time. He had had malaria in 1844 and possibly cholera in 1849, which supposedly sapped much of his strength until 1850 when he he caught cholera (again) and died. I'm sure both he and the Whigs would be conscious of that.
Lastly, the Whigs were already starting to fray around this time. Even if Taylor had been around to lead them, the Northern and Southern branches of the party are already politically diverging. And the economic boom that followed the Mexican-American War is still going to happen, perhaps even more so if Taylor quickly organized states in the west. That may seem like a boon, but in reality it undermined the Whig's messaging on the necessity of a proactive government. Having no official stance on slavery and having no economic messages meant the Whigs had little to organize around, which is why the party fractured in OTL. If southern states attempt some form of secession, I agree with you that Taylor would be quick to quash it and the South would probably see its political power dwindle. I expect in such a scenario that Taylor might lead some sort of unionist party rather than specifically reinvigorate the Whigs. However, all that said, such a scenario would violate the premise of this thread which was to avoid conflict over secession.