As already mentioned, freebass makes it easier to play left-hand melodies over a wide range. (If you really try hard, you can do quite a lot with the fundamental and counter basses and the occasional register switch change.)
Freebass also makes it easier to play sustained notes in the left hand without overpowering the treble, by providing a way to play with only one or two banks of reeds active. IMO it's a fairly fundamental flaw with many accordions, giving them such heavy bass voicing (and then we teach people to work around it by telling them to peck at the bass buttons rather than hold them down.)
That said... you can do a lot, both amateur and professional quality, with classical music on Stradella.
Gary Dahl has a book out, "The Classical Tradition", with simplified but convincing-sounding arrangements of 2 or 3 dozen classical pieces.
The Frosini compositions and arrangements were mentioned upthread (and if you are outside the USA, these are now out-of-copyright and legally freely downloadable -- he died in 1951.)
I'd also call your attention to the mid-20th century Soviet composers and arrangers. Nikolai Chaikin, among others, wrote extensively for Stradella-only left hand. I think of his Concerto in Bb for Bayan and Orchestra as a high-water mark of how far a Stradella instrument can go towards 'serious classical music'. Most of the later concerto writers have opted for freebass.
Alexander Dmitriev's arrangement of Rossini's "Largo al factotum" from Barber of Seville ('Cavatina Figaro') is also Stradella-only and can be seen in dozens upon dozens of Youtube videos.