I have fat fingers, too. :)
With my front and side-loading machines, I just tip them back in the cabinets to change the bobbins - as long as I've got to stop, anyway, I may as well swipe around in there with a pipe cleaner to de-lint.
The convenience of changing bobbins with the quilt still in the machine is a pretty big convenience. Pulling the quilt out every 35-40 minutes would be a pain.
I don't mind the drop-in bobbins when I'm piecing or making garments because there are breaks between seams where you're removing the work anyway. :)