Modes are certainly more than fantasy. I'd say they are of particular importance when trying to come up with appropriate back up to traditional session tunes.
I have a fair knowledge of music theory, including modes, but I still don't trust myself to play guitar in an ITM session. If, for example, the 'A' part of a tune is in a plain major key but the 'B' part is modal I can easily get caught out.
For most songs the basic chords are pretty simple, and it probably is true to say that the majority of songs in a major key can be covered by a common progression, so that's a good place to start your trial-and-error.
I, IV, V7 is probably most used - certainly it'll get you through the bulk of blues songs. *
I, vi, IV, V runs a close second and will cover most 50s rock and roll that doesn't fall under the I, IV, V7 umbrella. Certainly works for most doo-wop stuff! *
Any other chords will probably also be from the set included in that key, or there may be the odd passing chord - sometimes used to remove a clash between a melody note and the chord that would otherwise be held over that note. This can be a consequence of the kind of modal situation described earlier in the thread.
EZfolk.com has a great, simple chart showing the chords that occur in each key.
Chords will sometimes not sound quite as played on recordings because many artists will use inversions, substitutions and extended chords. Also, they may play in unusual open tunings that can make chord voicings sound pretty different. But the basic underlying progression, with all frills and affectations removed, is likely to be a standard progression built on the chords shown in that chart.
A friend of mine who gave me my early guitar lessons about 35 years ago used to say "Don't worry about anything that's not plain major or minor. The rest of it is just jazz."
Looking back he was dumbing it down for me with tongue in cheek (he's a good jazz player!), but it's pretty good advice when it comes to working out the basic chords by ear. At heart they will be simple.
A basic version of a song will usually work just fine with a major or dom7 chord, even if the actual chord played in the record that you can't figure out is a 13th chord.
Get the meat right. The exact seasoning will vary.
And for heaven's sake, don't accept chords taken from Chordie etc as gospel. The majority are innacurate - in some cases just plain wrong - although they can be a helpful place to start if you're really stuck.
(* In examples above, upper case = major chords, lower case = minor)