Should MBP 2014 CPU throttle without battery?

You maybe facing multiple issues here!

Your first issue is within the battery! The battery has sensors your systems thermal management system (part of SMC) depends on. To protect you and your system SMC will lower the CPU’s clocking. If you opened up Activity Monitor you will see the process kernel_task consuming a large quantity of your CPU percentage.

So you do need the battery installed (ideally working and charged). Let’s get a better view of things, install this gem of an app! CoconutBattery take a snapshot of the apps main window and post it here for us to see Adding images to an existing question.

You clearly have a second issue here as well!

You appear to be using the wrong display assembly! Your system requires a 2013/14 display assembly Apple P/N 661-8153. It will not work properly with the 2015 display assembly and you could also damage your logic board using the wrong one as the iSight camera is not the same. To add to it the iSight camera unit in the lid has a thermal sensor within it (which is why you are getting “to wait as temperature too high”) and that too will kick SMC into CPU Safe Mode!

Both need to be addressed to get your system working properly!

We still may have a third issue lurking… You made a comment about liquid damage! At some point did you get your system wet or have a spill within the keyboard and/or trackpad areas?