I previously asked this myself as well. But I just don't see it a Democrat being elected statwide in 2006. Maybe the race would have been within single digits, but Perry would have pulled it off by at least seven points or so.
You have a point, though we can also say the country still isn't totally polarized on a state level, given New England having an affinity of electing Republicans to the gubernatorial offices, while rejecting them on a federal level. Even over twenty years ago you could see a trend, with Bill Weld failing to unseat Kerry despite winning reelection by a historic margin two years prior. Today people like Phil Scott or Charlie Baker would've get utterly decimated if they ran for Senate.
They wouldn't win in a senate race unless there is a really terrible Democrat running, but Baker would give Markey or Warren a run. Now I know that Montana is a little different from all these states, but the fact that Steve Bullock has a real shot (and that Jon Tester won in 2018) still means the person itsself can be such a factor that overcomes certain partisan leanings, even at the senate level. I'm not sure this would have worked in Texas in 2006, though. Perry may have been not that popular, but he wasn't as unpopular as Christie or Corbett toward the end of their terms. At this point, the state didn't have a Democratic governor in over a decade and the last one was considered popular and still lost reelection by a fair margin to someone who didn't have political credentials other than being the son of a former president.