Trading in lots of 100 hasn't been required since I dunno, the 90s?

Assuming you're in the US there are several competent brokers that sell fractional shares. Any broker will do lot tracking and cost basis calculatioms for you, they're required to.

Rebalancing might be a pain, yes. I'd bet the drift isn't too bad most of the time, but it's probably effort every time you add or remove money. You'd want to build a tool to tell you how to add and remove to get closer to the index. If you can get the index weights and your holdings in a machine readable format, it would seem pretty tractable, but it would take time to setup; there's a reason funds have expenses, but index fund expenses are small.

I'm 100% invested in funds because it's a lot less work, but if you felt strongly about excluding certain stocks, I think it's pretty doable for say S&P 500. Tracking a total market index, or an international index would be more challenging. Bond indexes are also challenging to track, even for bond funds.