In a lot of cases, they aren't left with much of a choice. Many chips aren't in production any longer, either due to them being custom chips or due to them serving a need that the market no longer has. Stuffing everything into an FPGA isn't really a solution in this case since it effectively makes it a hands-off machine.
What do I mean by hands off? In terms of software, it doesn't make much of a difference. You can still develop for the machine and it will appear to be the genuine article. In terms of hardware, it is a different ballgame. At best, slots and ports may be exposed so stuff can be added to the machine. It will be a bit like using a modern desktop, albeit with the opportunity to develop your own expansion cards since the expansion bus can be more accessible than PCI-e. On the other hand, most modifications to the hardware itself must be made through the FPGA. The FPGA route will be more flexible, but it requires an entirely different skill set. Relatively few people have the skill or interest to deal with FPGAs, particularly if they are seeking something more comforting than modern hardware.
How is replicating something like the video chip with an FPGA somehow acceptable? Presumably it is because it has to interface with the rest of the system in a conventional way and since people were unable to modify the video chip in vintage computers anyhow. Since it is interfacing with the system in a conventional way, you can also mess around with the video circuitry surrounding the chip.