Uh, if we're going by film / TV canon, then:
1. There are quite a lot of weapon types, including shield-piercers, cloaking devices that make Phase Cloak look lame, hacking devices, boarding via teleporters, shield systems that "re-tune" to resist damage, etc., etc.; it's actually a pretty rich universe, in terms of weapons and counters. They aren't invisible, either; I'm really not sure where that idea comes from; Trek's weapons are quite visible and flashy.
Unless we're talking about turrets with that statement (where that's not entirely accurate either, but largely is); basically, Trek ships just have invisible Built-Ins and wouldn't have Hull Mods, etc.; they're purpose-built and don't get "field modifications" terribly often in canon.
2. The problem with this, especially the Romulan Cloaking Device, is largely that you'd need to build some pretty specific AI support for it, since Cloaking Devices don't work much like Phase Cloak at all (they don't make ships invulnerable, merely invisible, for example).
3. Phasors and other Beams would do Hard Flux; that's not a biggie to implement, though.
4. If you wanted a super-accurate Trek, then most combat ships would have 4 shields, not just one globe shield; that's doable though, with some Station-like bits and a little scripting, I think. What would be interesting is doing the lenticular shields that are pretty common in the Trek universe.
5. I think that the idea that it would play badly is largely wrong; it would just play very differently and need a lot of tuning for that experience. Making vaguely Trek-like ships as a Faction wouldn't really do it; we're talking about a TC here, I think, which is a lot of work. I'm not passionate-enough about Trek to do this, but if somebody did good Trek sprite conversions and built the ships / weapons, I might consider building some of the code for it.