You're funny. Why do you make the following assumptions:
1. Moving to another city-state would be easier than moving to another country (aside from language)?
Seriously? Isn't this obvious? Language, for a start, is a huge barrier. No wonder same-language immigration is more common.
And... don't you have friends, family? What about culture? Eventually properties you want to keep etc. There are so many barriers in long distance immigration, you must be too cynic to even ask such question.
Just compare the percentage of people who don't live in the same city/town they were born with the percentage of people who don't live in the same nation they were born.
2. City-states wouldn't merge for security and/or economies of scale?
I'm not assuming that wouldn't happen (although the actual reason would never be economies of scale, that might be an excuse perhaps). I'm just saying that if it happens, it will be a change from a better configuration to a worse one. A regression.
3. Free trade between city-states would magically be optimal the way you see it?
Not sure I understood your question. Free trade is always optimal.
If you are wondering if free-trade would really happen, then well, I say it would, because these city-states would not be able to afford creating large barriers to trade. And the more free-trade there is, there richer the city-state would be, attracting more immigrants as I explained before.
But, even if you believe free trade is bad and we should only trade locally (what's false, but let's take it for granted), then still you have to agree that the city-states who raise such barriers would be more prosperous, and others would copy.
The point with competition is that it creates incentives to improvements. We don't even need to agree on what "improvement" means to see it.
4. Trade and travel across city-states would not be fraught with transit fees, tariffs, taxes, tolls and so on?
Again, I'm pretty sure the city-states who follow such path would prosper less, and thus competition would end up killing such bad policies. But the same thing I said above applies. If you believe free immigration is bad for the economy, it should be clear to you that the city-states which allow it would have economic issues, compared with those which don't allow it.
By the way, do you know of a single empiric counter-example to this theory?
Can you point a micro-state, encrusted in a larger state, which is not better off than the large state? All examples I know are better off (Monaco, Lichtenstein, Singapore etc). Even when we take very-autonomous-but-not-really-independent regions like Hong Kong, Macau or Gibraltar, the principle remains.
There might be a few exceptions as for every rule, but I don't know any. It's clear that, in general, micro-states are better off than their neighboring large states.