Why do we need a SignalTapII that stores data on FPGA instead of...

Here are some thoughts:

SignalTap is most popular especially for beginners who can view their achievement for real. It is easy, but needs care with clock(s) and fpga fmax. Practically not useful for large project testing but only minor debugging.

sources and probes is useful if you want to debug without changing fpga build (for build sensitive cases).

logic analyser Interface editor: never used it but sounds it is external analyser instead of signaltap and so must be far more more powerful and does not need changing fpga build