So far, I haven't had that experience with both my main city in Sinya Arda and my baby city in Felyndral. I put up my own trade requests when needed and they usually get picked up by the neighborhood, or the fellowship (have you joined a [semi-]active fellowship with exciting flavors of trade?).
As for personal experience with active t1-t3 trading in Sinya Arda, my neighborhood does indeed trend towards t3 goods with cross-trading. If there was a shortage of anything, it'd be t2 (and the trading activity in that tier is still healthy). I've got at least one FA-dedicated city nearby that pumps out t1 goods like nobody's business (and boy howdy do those cities look awesome in a clean-lines industrialized way), so a lot of trades that aren't between the t2's are usually cross trades
towards that tier. When I talked to the higher ranked people in my fellowship, they've lightly commented on the complete opposite: t3 stuff is much harder to come by and that they're swimming in t1 goods, and the fact that I'm in a neighborhood that trends towards t3 is an awesome thing to have.
Your personal experiences
will vary depending on the server, fellowship, and neighborhood you're in. The best situation to be in, I think, is where the shortcomings or strengths of one can beautifully compliment the shortcomings or strengths of the other. Where all goods regardless of tier, are perfectly fungible in any direction you please. In that regard, I feel truly blessed.
As for practical solutions that doesn't involve being more proactive with trading,
writing a complaint about being in a dead neighborhood, or upending your current social network and/or friends in your current fellowship to join another that does the sort of trades you need for your city? As has been suggested in a post before this one, try changing the ratio of productions to favor the tier that you can cross-tier trade towards the easiest. If you've been actively doing Spire, you should have a few teleport spells to stuff the not-as-needed-but-still-valuable manufactories into cold storage so you don't have to recreate them in the event your adjustments didn't do what you want.