As long as each mage has more than two paths, the mage turn argument is valid. Every three path mage searches three paths every two turns. Every site search remote spell searches one path every turn. The more 3+ path mages you send out searching, the larger the more turns saved. You're not thinking.
This assumes no wasted turns for backtracking, etc. This also assumes that you value all gems equally. This
critically assumes that you'll have multipath mages in convenient, non-overlapping combinations for all paths you're interested in (which is very much an unreasonable assumption grounded in pure theorycrafting, especially since a non-trivial number of nations have at most two-path or two-path plus holy or random-path mages - and since you aren't always going to be searching for sites from mages you can just recruit more of). And if you're allowed to throw more mages at the problem, you're still not getting away from the fact that each mage only searches one province every other turn; more remote sitesearchers mean more every-turn searches, and depending on searcher path levels, you're not missing 10-40% of sites (and those being missed are more likely to be recruitment or multigem sites) - and you're getting the gems sooner. You're not thinking either.
OTOH, remote searching is range-limited - for some paths brutally so. And it requires a modest research investment before you start. And most paths require at least two levels to cast the spells, and all need seed gems to start searching. And that of course is beyond the normal gem and potential time cost.
Neither option is all good, but neither is either all bad. A hybrid approach is best. Sweep with multipath mages as is convenient and possible, remote sitesearch for thoroughness as you can and as circumstances encourage or demand. I
entirely agree that in general it's better to base your sitesearching on manual searches. But remote sitesearching is not the worst thing evar, nor so grossly inefficient that you'll wreck yourself if you use it regularly, etc. It's caffeine, not crack. It's bad for you to use too much of it, and if you use it in exclusion to everything else it's inefficient and will give you a headache - and if you've used too much, stopping using it will give you a headache. But it has its place and it has its value.