I wonder what you define as a hit, I've always been a dreamer. The Eagles had many great songs but the early hits were defined by their inclusion on Their Greatest hits Album 1972-1975. Bernie had left the band by then so he didn't have any tracks on it (Witchy Woman excepted)
I'd suggest that they'd be one, probably two if he'd stuck around 'til after it's release, (I wonder if he was aware of it before he left), which would have required it to be extended to a double album or be a weaker single hits album. Either way, I don't think Their Greatest hits Album 1972-1975 would have had the impact that it did.
Desperado is probably my favourite Eagles song but it wasn't a hit. I couldn't imagine an Eagles hits album without Desperado included. Leadon songs like My Man and I Wish You Peace may have become major Eagles hits, had they got the exposure of being included on the Greatest Hits album.
Back to Randy. The Henley, Frey, Meisner harmonies are peerless imho but I'm not keen on Randy's lead vocals or maybe I'm not keen on the type of song his voice fits best. Adopting a thesbian analogy, he's one of the great supporting actors but hasn't the charisma to carry a lead role
I would have loved to see and hear him doing anything onstage during the HOTE Tour.
I believe the definition of a "hit" in the US is a single that spends at least one week in the Billboard 100. Using that criteria, the only Eagles "hits" to be excluded from Their Greatest Hits 1971-1975 are Outlaw Man and James Dean.
The problem that Bernie and Randy had was that their songs weren't chosen as singles. Interesting to see that apart from Witchy Woman, it was always Glenn right up to Best of My Love.
The funny-unusual thing is that Don & Glenn helped make TITTL a hit, signature, song for Randy. But, that was the seed of what led to Randy leaving the band.
I do remember reading decades ago that 'Randy Meisner shouldn't be allowed to do lead vocals' which I strongly disagree with. (Please don't challenge me for my source - no idea.)
He has a distinctive voice for sure, and I can understand it being love or hate for many people. However, speaking personally, the last thing I want to hear is people with anodyne voices singing anodyne songs. I like singers to have something distinctive that makes them stand out, and be instantly recognisable.