Looting is different from Brainstorming and doing it at instant speed is a very real difference to the game - consider Snapcaster Mage.
Agreed, looting is different from brainstorming; usually looting is inferior, unless you have some graveyard tricks, because you (often) see fewer cards and don't get card advantage. I think the lack of card advantage is the most important difference, one which is crucial for blue decks.
Phasing a creature out at instant speed allows for interesting combat tricks
Usually not relevant in a vintage blue deck, unless things have changed drastically since I last played.
While JTMS has a game winning ultimate, I have fought against it and won a few times. Taking 3 turns back to back will usually end a game of Vintage.
It sounds like you're presenting an exceptional case (wining versus the Jace ultimate) as a reason against it. The Jace ultimate will usually end a game of Vintage, too. Taking 2 extra turns requires other stuff to win with it. Admittedly, you probably will win if you get to this point, so the difference in value here isn't as great as the other points.
I think I like Teferi over JTMS in the current Vintage meta but that may just be my opinion.
By all means test it out and let us know!
I don't want to rain on anyone's parade, but JTMS seems superior in almost every way.
Brainstorm each turn > Loot twice each turn
Bounce a creature > Phase out a creature
Game-winning ultimate > Take 2 turns
Yes, there are some subtleties that I'm ignoring here, but the new Teferi is pretty much strictly worse.
I haven't liked BSC for a long time now, though I don't get much of a chance to play Vintage nowadays, so what do I know. The thing is, he's vulnerable to Dack Fayden, JTMS, and now Oko, three big planeswalkers that other blue decks could reasonably be playing. Not to mention STP.
I've always had good success eschewing Tinker entirely; my playstyle tends more towards hard control. Conversely, I can remember several times my opponent had Vault or Key in play, which I was able to ignore entirely because it did absolutely nothing on its own. But maybe this is just me.
Anyways, a suggestion you could try.
Everything that facilitates the things I don't like, and inhibits the things I do, is unfun, broken and format-warping.
Conversely, everything which facilitates the things I do like, and inhibits the things I don't, is fair, fun, interesting, and helps maintain Vintage MtG as a vibrant and strategically deep format.