You are completly right and that's exactly why 1* will quickly crush 2* and 3*. You need premium gacha for 2*+ shards. And the stats are not lower (or in a very minor way, which will be quickly forgotten when you will have 1 or 2 more stars).
You get also 1* shards from friend and basic gacha, and among them, you get Trisha, Naladia and Elnora shards while farming the hard mode (there is a 4rd farmable character as well, but she is earth/archer, which is a doublon with Trisha being earth and Elnora being an archer).
Trisha, especially, is a 3* for free (since you get enough shards just by login during the first week) with a 3* special weapon (from the login and another achievement). So she is 2345345353% worth it to farm.
Tomorrow (3rd day), she will be 3*; I have already farmed 30 shards.
However, an exception can be made for Claire (3*). She heals, and it's rare. So, you may want her in arena and/or in tower of trial.
As for pulling, I will spend my first 6K diamonds into the equipment gacha. With a little luck, I will get a pair of wings. After that, yeah, I will pull the premium gacha, just for the sake of collection.