Hey Alex, fancy seeing you here :)
I'm going to agree that the "if you want me, do some work first" thing seems a bit overkill. For me, usually just a single sentence asking for salary range and job description gives me more than enough to figure out whereabouts in the spectrum they are.
This is the way I think about it:
1) there are different types of recruiters. At least in the city where you are, I can tell you that there are actually some good recruiting firms that consistently send appealing opportunities while avoid wasting your time with emails about lowballers, if you just spend the 30 mins upfront to chat with them about your expected salary range and specialization. These recruiters understand that there's an entire subsection of the workforce that is very capable but has zero online presence, and they build their own moat by connecting w/ professionals directly, to build a long term, high quality, proprietary network. Being part of such networks and having the recruiter sift and prescreen jobs for you can be valuable. For one-off linkedin cold mailers, the signal to noise ratio is generally pretty low IME because they optimize for volume. While they can give me data points about what lowballers offer, I personally haven't gained anything from this info, so I'd optimize elsewhere. YMMV.
2) you can often infer salary range from the company name and job title alone. As a rule of thumb, if it's an no-name company, they're almost always going to lowball if you're at senior level. If your goal is to raise your salary quickly, then rather than looking at sideways increments, you'll want to target "obvious" upgrades (e.g. if one is junior, look for "senior" roles; if you're senior at a local non-US company, look for US-based multinationals; or just go for broke and try for unicorns exclusively)