Is it worth it to replace T1-11 siding just to install house wrap?
I looked in the 2012 residential building code book I have and there is no exception for the building paper/tyvek. It is to be used in all instances of siding. Whether it be brick, cement board, shingle, or T1-11(panelized covering)
I added the term panelized covering because in the 2003 CABO and perhaps earlier, for your case, that was the code book used to govern building practices. I had a lot of that book memorized for the areas I needed like siding, headers, stairwork. My recollection for that time, that the building paper layer was not needed for panelized wall covering. What I claim, may or may not hold up to scrutiny, since my copy of that code book is buried away somewhere. It also depends on your area you live in and which code book that was followed, since there were a few different code books that were used back then. Nowadays since 2012, I think all building everywhere in the states is using the ICC IRC for single family homes.

In your case, if there is window flashing missing, and places rotting where the wood siding is too close to the ground or covered by shrubbery where the moisture can get in or is constantly present, building paper will not help.

In my experience, if the material is installed properly, with all proper flashings, seams nailed at the studs, proper laps at the studs, and I "back prime" my cuts and bottom edges so water will not wick up or into the layers of the T1-11. Your siding will hold up.