They don't serve the same purpose.

A liquidity pool stabilizes the price at anything. If the price is $2, a liquidity pool will 'stabilize' it at $2, in the sense that the liquidity allows you to trade more at $2 without moving the price, potentially even making it harder to get back to $1. That being said, liquidity pools provide liquidity, and liquidity is definitely useful. If people think we should subsidize that (certainly a case can be made), then go ahead and make a proposal to DHF and try to get stakeholders to vote for it.

The HBD stabilizer, which is support by the hbd.funder comments, stabilizes to the peg. It's trades are conditional on the relationship between the peg price and the market price. It doesn't actually provide liquidity particularly, though at times it can have that indirect effect.

These are two different things.

Finally, as @blocktrades has said many times, the hbd.funder comments also fund DHF itself (since all payments to HBD stabilizer are then eventually returned to DHF). That has nothing to do with liquidity at all, or even HBD, but is completely different purpose for the comments and reason why some stakeholders vote for them.