I don't think anyone has said jazz tunes supposed to have 7th chords everywhere. But I do agree with you. Many jazz tunes (especially old ones) uses 6th chords instead of 7th chords. And yes, a D/C is not the same as a C13#11, etc. Removing one note in a chord changes its color. In some cases they can substituted, but not always.
iReal pro has a good chord library, but there are some important chords missing (I've posted a list a while ago). Yes, it would be good to have a C triad with a #4. Using with other bass notes (slashes), it could help creating many other chords