Only certain brokerages offer fractional shares, and then with fractional you don't get the full benefits of a full share (ie, voting). Further, it's a mental stoppage. I'd never buy 1/3rd of a share, but I'd buy a share that was 3:1 split.
That being said, yes, I cannot afford to buy a shingle share in one go any longer. I had set aside $500-1k a paycheck, and that got me a few shares last year, but is now not even a full one. I'd have to save for three months to buy one share, and that's not even saying the share would be that same price in three months.