I find time-clocking incredibly irritating, as I may be inspired to a solution or want to fix something outside of hours, which is pretty common for me. And similarly, I don't want to feel bad about if I am doing something wrong or not the most efficiently, but still charging full price for that time. Possibly the most irritating thing for me in times I was on hourly was arriving at work a few minutes too early to clock in and having to twiddle my thumbs, or having to determine whether or not something I wanted to remote in and do met the official terms for being paid in after hours time.
My personal feeling leans towards paying for "a job well done", and leaving it on the idea that if you're doing your job well, I'd like to believe nobody will question how you spent the hours you were doing it.
Being paid while on the bench makes a lot of sense if they feel you're valuable enough to retain, and time to actually spend training is pretty nice when you can fit it in, and obviously works to their benefit.
Then there is no problem with just billing the spent hours without any fudging one way or the other.
- A lot of people at the company would feel guilty and put in free hours to the client. (They would usually also get rewarded with excellent customer feedback.)