Sure the load can be very spiky and you have to sample fast enough to accurately integrate them. but that's doable given sufficient caps. Of course you'd end up with some filtered average instead of the instantaneous power, but that would be no good for a text display anyway.
When your range is from nano amps during sleep to spikes of several tens of amps you will not find a voltmeter with a range big enough to work with a single shunt. You need several shunts and switch between them very fast. That's what devices like the Joulscope do and why they are expensive.
Sure the load can be very spiky and you have to sample fast enough to accurately integrate them. but that's doable given sufficient caps. Of course you'd end up with some filtered average instead of the instantaneous power, but that would be no good for a text display anyway.