Even better, charge for entire projects or engagements, start to finish. The more competent and efficient you are, the more you will make per unit of time.
Integrity and foresight are the “premium.”
Besides hourly, have you tried daily billing? I rarely see this mentioned but I think half day billing works well: unlike daily billing you're not forced to work the full day for one client, and the timekeeping can be less granular so you can focus more and worry less about eating/explaining hours.
I've seen people advocate weekly billing (and even monthly), but then what if you can only commit to a few days some weeks?
Precisely why independents exist.
All of that other stuff is your distraction. You can have a mixed strategy. You can tune and innovate over time. Think things through and find what meets opportunity. Clients want work done with out the pain in the ass. Being direct and easy to deal with is “why me” in the first place.
You can invoice in blocks and pre bill ~25% as a retainer of necessary. You work through blocks of hours or features and send “pay the amount of” invoices every week (or as agreed) subtotaled from the projected original.
The first (or routine) invoice is just their professional promise to pay you as agreed if you do the work. Periodic or batch “pay amount of” invoices notch away at these. Keeps everything clear and hassle free.