Yes. I have a two line bash prompt: the first line with a whole bunch of info like the exit status of the last command, the number of background jobs, the hostname, current username (very useful when you have 5 different ssh sessions to different machines), and the current working directory.
In real world usage I have experienced almost no loss of utility from only having 50% of my command history on screen. In fact, given how many commands are just ls,whoami,jobs,pwd, that info gets condensed into one line.
Mine's very similar, and includes the current date and time; it also wraps onto the next line and starts with a # (mostly because I'm an idiot, and have burned myself by copying-and-pasting an entire-line-plus-newline and ran a command instead of just copying it in order to edit it.)
It's actually dynamically generated by my .bashrc so that different servers have different colors; at a glance, I can generally tell whether I'm on one of my machines, or on a work build server, or an amazon ec2 instance.