Well, I'm OLD and I went to SCHOOL, but I don't think that qualifies me as an 'OLD SCHOOL' player ...
The most left hand bass I ever played was while I was playing accordion, and for the first few years with 3 to 5 piece groups I was the 'bass player' ... later on, with the band we had for 26 years, I switched to Cordovox and the bass player - who was the featured vocalist - would put down the bass and I would play left hand on the Cordovox while he sang ...
Unfortunately, I never applied myself enough on the Rhodes or subsequently on an arranger keyboard to play left hand bass ... Doing OMB work - depending on the venue - I will sometimes play a ballad first with no tempo, adding arpeggios or polyphonics, and then play the song with some rhythm accompaniment ... Basically, the purpose of my keyboard is to accompany my main instrument, my voice ...

And, as others have said, I get greater pleasure playing along side other musicians, and backing myself or other vocalists on keyboard ...