The reality is both Software and FPGA emulation can be done very well and with very low latency, however to achieve this in software you generally require high end power hungry hardware.
A steam deck can run a highly accurate sega genesis emulator with read-ahead rollback, screen scaling, shaders and all the fixings no problem, but in theory the pocket can provide the exact same experience with an order of magnitude less power.
It's not quite apples to oranges of course, but the comfortable battery life does make the pocket much more practical.
For a full computer like the Steam Deck, you have to deal with preemption, display buffers, and more, which _will_ add latency. Now if you went bare metal, you could definitely drive a display with super low latency, hardware accurate emulation, but obviously that's not what most people are doing.
mA? You're not very convincing here.
A potential advantage of an FPGA over a dedicated chip is that any unused functions can just be left out, saving power dissipation and logic resources. This is the (largely unrealised) promise of Reconfigurable Computing [1].
More capable FPGA's like what I work with run in the hundreds of MHz and that's when you can draw 100W on a single chip
Getting a large design that passes timing at that frequency with the Cyclone V fabric is unlikely, however.
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The distinction here, being that more capable FPGAs can get up to the 600MHz+ range, and actually run a full design at that speed.
Guessing that's a generalization of using it as the main CPU. There's a Lattice ICE5LP4K FPGA in the iPhone7.