People are mentioning redirecting the belay through the anchor doubles the load, but doesn't the lifting of the belayer (assuming they are hanging below the anchor) make it more dynamic, likely sprading out the impact over time. I have always been a believer in bomber belays, which makes the whole question somewhat mute, though I understand you may not have that with ice.
Also, belaying the second up, if they fall, it is not likely going to generate a lot of force. If you are worried about the belay holding then, I sure wouldn't want to be relying on it when they climb through. Once they are leading and have clipped a piece, how would belaying through the anchor increase the force? If they fell before the first piece, I would think you would particularly want the catch to be dynamic. If my leader took a fall factor 2, I would feather the belay.
Let’s focus on just one situation here, belaying a 2nd.
If you re-direct the load strand through the anchor (or a high piece set above the anchor), and the 2nd falls generating a force of “x” on the load strand, an equal force of “x” must be applied on the other side of the carabiner to prevent rope from moving.
This, equals 2x. Yes, the belayer moving may soften the catch a little, but “x” still needs to be applied on that side of the carabiner to stop “x” on the other side. That means that carabiner/pro sees 2x. It’s pretty simple physics really...
If you are directly belaying off the anchor, with Munter or “plate” style device, that carabiner/pro only sees 1x.
I hate to mention this book but FOTH diagrams this well...
Bottom line, as long as the “high-point” is absolutely bomber it shouldn’t matter, EXCEPT if you end up needing to create a haul system or escape the belay... as Strand will attest this is a rare event... however I choose to direct belay because it is
more comfortable, easier to take in slack quickly (depending on the device) and with many devices I can be hands free in-between yarding slack, allowing me to eat, drink, take pictures, scratch my ass, or whatever else needs attending...
Talking about Factor 2’s if the 2nd climbs through is a separate topic IMO...