In a tenure-track position application; Is it appropriate to ask for recommendation letter from a professor for whom I only served as a TA?
It depends on the school. At a SLAC (small liberal arts college), the hiring committee members will pay more attention to teaching experience and may be more willing to be impressed by a Big Name®.

At a R1, faculty are not only inoculated against Big Names®, but they have enough experience with individual Big Names® to read between the lines of otherwise blandly positive letters with hermeneutic vigor.

I've been repeatedly surprised by my senior colleagues discussing letters from other Big Names® with "he only wrote two pages of song and praise? He must not have liked that person" or of a fairly damning letter with, "she's a grouch. The fact that she wrote at all means that this person is brilliant." Context is important.

A letter that spoke only of your teaching and not of your research would be seen as faint praise in this milieu.

Note that I'm in the humanistic social sciences at an R1. Your mileage may vary.

TL;DR: save the references from this person for SLACs where the praise for your teaching ability will be seen as a strong positive.

Also note that at larger R1s, we are familiar with the difference in writing styles between American (where everything is excessively effusive) and European/Asian letters (where a strong letter of recommendation reads: "Jon Smith was a member of my lab from 2005/10/1 to 2012/5/1. His work was perfectively adequate with no complaints. Sincerely, XX"). Smaller institutions may not have that experience and in those circumstances, you may ask one of your American letter writers to include a short paragraph noting that European counterparts thought highly of you but that might not show up in the letters in the hyperbolic form we are used to in the United States.