An independent miner with an average affordable rig might find somewhere on the order of one block per year on average. This means that due to variability, a good proportion of miners would not find any blocks at all within the lifetime of their hardware, and give up forever.
If low-income-variability pooled mining becomes impossible, then my guess is that mining will be centralised to people who run purpose-built datacentres full of miners, not the casual users.
AFAIK, that's already happened. The difference is only that mining pools owned by independent entities wouldn't be able to collaborate. So you'd be more likely to have e.g. 5-10 big pools, as opposed to 2.