Ever had a rechamber? If so, did you find the barrel still liked the same bullets? I mean re-chamber to a larger capacity round. Say my 30-06 likes 168gr TTSX bullets, if I had it punched out to 300 Win Mag, is it likely to still like (or NOT like, such as 180gr Power Max) the same bullets? Or the 200 +/- change in velocity going to throw that out the window?

On a change like you suggest, .30-06 to .300 Win Mag, you may not be shooting the same powder any more. And that's a big part of the equation too. (Also, you'd also have to get a different bolt head for that change.) So maybe. Try it. But the velocity in a bigger cartridge may be more than a given bullet can handle.

LWD

I rechambered a 7mm RM to 7mm STW and did not note any discernible change in overall accuracy. I can't recall whether the same bullets performed the same, just that it was no more difficult to work up an accurate load after as before.

same bolt head, its a Win Classic, just opened up

I don't think punching out your 30-06 to a 300 win is all that good of an idea. Unless you are going to cut off the complete chamber enough to support the new chamber reamer's pilot. W/O doing that it is going to be almost impossible to get the reamer cutting w/o chattering and once it starts to chatter it's pretty much over for a real good chamber job.
My experience is that just changing things like bullet depth, type of primer, powder and/or charge will all change the guns accuracy. By changing the chamber you are changing everything except the quality of the rifling in the barrel. If it shoots to your liking now.. why not leave it alone?
Just my 2-cents, Joe

SxS couldn't you just us a boring bar to open the 06 chamber enough to allow the WM reamer pilot to reach the bore? You would have to stay under final reamed dimensions but I think I have done that. I may have used my compound on an angle to do it, but am pretty sure I have done that rechamber before.

Rechambering .30-06's to various .300 magnums has probably happened at least a million times since the 1930's. Thousands of Springfields were rechambered to .308 Norma. While it is certainly possible to do a bad job, reaming out a .30-06 chamber to a belted magnum is a simple process that is successfully done by competent gunsmiths every day.

That said, it is usually a poor idea unless the rifle has at least a 24" barrel and more velocity is truly beneficial in its use.

I had my .30-06 re-chambered to .30 Gibbs, and other than working up new loads for the Gibbs, the same bullets were just as accurate.