Any miner paying with a higher difficulty either needs idle hashpower, or self-increase their own difficulty at the possible opportunity cost of losing an entire block's income to another miner who doesn't care about changing the block size.  The potential loss does not economically compensate for size increase gains in most cases, when you consider the variability of blocks (they come in bursts and pauses) and the fee income that would be associated.

Miners have more to lose paying with diff than they gain -- unless the entire network colludes out-of-band with ~90% certainty, by collectively agreeing to increase the block period by collectively agreeing with pay-with-diff until the globally desired block size is reached.  At that level of collusion, we can create far more simple schemes to increase block size.

Pay-with-diff will either not get used, or lead to radical short term block size (and thus fee) volatility.  It is complex & difficult for all players to reason, and a Rational game theory choice can be to avoid paying-for-diff even when the network desperately needs an upgrade.