So the cons outweigh the the pros?
Yes, I would say so, unless you're going to compensate the "losses" as mentioned by means of preamplification, whereby the "preamps" should reside as close as possible to the antennas, to prevent cable losses. The solution being quite expensive of course, taking the amplifiers and their accompaning power supplies and "Bias Tees" into account.
Another way might be to use just ONE amplifier BEHIND the splitter, but depending on cablelenght between the feeding antennas and the splitter, cable losses have to be considered again. "Noise", as added by the feeding cable, will of course too be amplified, finally degrading the "signal to noise ratio" at the receivers input.
As the "individual" antennas normally will be situated "far" from each other (as otherwise does not make sense) this "solution" appears not to be very attractive.
Regards,
Karl