I use the tinys all the time, actually. I use them as scouts in the early game - long range, to try and contact every other race as early as possible. When I have, I set them all to auto explore. By the sensors 3 stage, my economy's pretty good, and I can upgrade them to survey scouts. They're spread all over the map, so even though I could make bigger, faster survey ships back home, the scout that's already on the other side of the map will still get to the anomaly faster than the small hull or cargo hull which has to cross an entire map to get to that same anomaly.
When the anomalies run out, I set them again to auto explore.
When I've pretty much discovered the entire map, my economy's normally going very strong, and it's faster to just upgrade those scouts to carry constructors than it is to waste a turn with a planet's starbase building a cheap constructor. Depends on my miniturization, but a tiny with a constructor module, plus sometimes an engine, no defenses, it does the job, and only costs 200 or 300 per ship. Then I have a huge swarm to constructors - whether they then come back home for economy bases, or shore up my borders with influence bases, etc. I'll even use them up back home, if I don't need the other two, setting up military bases with ship speed +2/-2, just to speed up getting attack ships out of my territory, and to slow down enemy fleets coming in.
Considering I can quickly get up to the point where I can, when I don't need my planets for military, pump out tinys with constructors and a single engine in a single turn, they're incredably useful - I normally end up with a whole range of fully maxed starbases of all sorts spread around my mid-game territory.