Indeed. The reason to use things like dichro's instead of ordinary prisms is mostly a practical one. Even with materials with higher refractive indices the whole setup would be impractically large to transport, and be sensitive to thermal expansion of all materials used possibly requiring re-alignment for every time you use it.
So in short: Yes, you can use ordinary prisms to combine 3 laser beams into a while one, but it would just not be overly practical. If you want to do this for a science project, museum demonstration or something like that, proceed.