A few notes on the bullet-ed points.
1) If you high pass below the lowest fundamental, you will lose nothing. Setting the filters too high will of course cause a lack of bass response. It takes some analysis to determine the right point, and a good, full range, speaker system to confirm you are not doing more harm than good.
2) Phase shifts only occur at the point of the affected signal, so you don't need to worry too much about the higher frequencies becoming out of phase, which is where and audible problems would occur. Of course linear phase eq's were created to avoid any problems period.
I use high pass filters often for high frequency instruments and sometimes on the master buss, cutting the energy below 30Hz where not much useful musical information occurs. To use it on every track is overkill and rather pointless.