I don't think anybody disputes that TR would have won - after all, his stand-in did. He would indeed probably do somewhat better than Taft, perhaps squeezing Bryan down to around 41% against OTL's 43.5%.
My point is that there isn't the slightest likelihood of his winning big enough to put the Democrats out of business and triggering some sort of party realignment. His big 1904 victory didn't do any such thing, so there's no reason to suppose that an almost certainly smaller win in 1908 would be any more likely to.
In particular, it isn't likely to make any serious dent on the Dems' position in Congress - more important than the Presidential race if any kind of realignment is to be possible. OTL, despite losing heavily to Taft, they actually gained eight seats in the HoR (plus three in the Senate) on top of the 28 gained in the 1906 midterms. and in fact would not suffer a net loss of seats in any House election until 1914. If TR's 1908 victory is slightly bigger than Taft's was, then the Dems may suffer a modest loss that year, but there's no reason to think it will be anything major. In short, the Democratic Party stays firmly in business, TR or no TR.