The thing is, we probably should have done this for quite some time - using the reward pool to incentivize effective and relevant work on Steem.

We did in the early days. I'm not going to claim it was the main or only use of rewards but there were very significant marketing initiatives, third party integration projects, etc. that were funded by rewards. There were a number of Steem apps proposed and received significant funding (although unfortunately some were scams or simply did not have credible roadmaps; the community needed to develop a bit more sophistication and skepticism).

Things went downhill from there.

but work focused on Steem should be n°1

Damn right. For the millionth time I've said this, investors are paying for rewards. This only makes sense one of two ways: 1) Investors see it as a way to generate personal ROI and siphon rewards back to themselves via self-enrichment, spamming the chain in the process and ultimately everyone chasing their tail and getting nowhere; or 2) rewards are allocated to purposes which add value back to Steem increasing the value of ones investment. Everything else is inefficient leakage which discourages (and should discourage) people from investing.

There is a lot of room within 'add value back to Steem'. That can include sponsoring pure content such as art, writing, etc., or even donating to charity, but only when calibrated to the level where it helps promote the Steem brand (and, here too, curation quality is so important because sponsoring generic crap content and/or scams hurts the Steem brand). It can also include a faucet type functionality where new users are able to earn some rewards as an incentive to join. It can include sponsoring app developers, but only to the extent that those apps are successful in bringing users, investors and growth back to Steem.

If we can't get any of this to actually work we should turn off rewards, pivot to a different model, and at least stop chasing investors away with useless inflation.