You don't actually benefit J1 ships by forcing them to charge twice as much to carry something two parsecs in two jumps as you force J2 ships to charge for carrying it the same two parsecs in one jump.
And why would the Imperium want to benefit J1 ships? J1 ships already have a niche they dominate: carrying goods and passengers back and forth on 1-parsec routes.
No one, because all the trade from the small world will be carried on J1 ships.
Ok, I'll rephrase my question: who will buy a J1 ship if not because it can give more return to inversion than a J2? And this is only true if prices are per jump, instead of per parsec.
J1 ships are handicapped enough, and the only way to keep them running (and so, not to abandon those small systems) is to give them some advantage. The fixed prices, that allow them to run at more benefit per investment may well be it.
If a set of game rules create a problem, I think it ought to provide guidance for solving that problem too. Whenever I hear "Well, the referee is free to step in", I know there's a bad rule being defended.
(...)
Assuming that the Imperium does tax individuals, which does not seem to be the case. (That is to say, there's no evidence whatsoever that it is the case and I for one do not think it would fit the Imperium as portrayed to establish that it did. But this is edging into opinion territory.)
Then you'll think all RPGs rules are bad, because the quote
"Well, the referee is free to step in" is in on the introduction of any RPG I've seen till now... (in fact, I think is one of the basis of RPGs)

.
Now seriously, to change any aspect of the economical rules set in Traveller (or any other game, for what's worth) is seriously altering its balance. As you say, there's no evidence about Imperium taxing individuals (at least directly, it taxes them through planetary governments), but I think is logical to think the Imperium somewhat taxes ships and trade (see that I don't talk about taxing people, but the ship as if it was a company, though maybe I was no clear enough on that). I couldn't find a single place in the rules where those taxes are explicited, so, either space travel is tax-free (and I have a hard time to believe that) or the costs are assumed featured in the operating costs. As this is not explicity featured in the game and I assume it's featured in the costs, if you alter the costs it could be alteres, but I'm not sure how.
Yes, if you're a tramp merchant who just happens to have bought a load of speculative goods that you believe you can sell at a profit on a world two parsecs away, you'll probably see if you can pick up something to increase your profits on that world in between. But what does that have to do with a price fix? And why would the Imperium care if you visit Smallworld or not? And if it did care, wouldn't you be more likely to find passengers and freight if you were allowed to charge Cr600 per ton and Cr6000 per passenger?
About why should the Imperium care about this small planet, why do governments care about small villages? perhaps because they are also citizens? perhaps because they want to keep them integrated (as much as this word can be applied to the Imperium)?
About what has it to do with fixed prices, the only answer I can give you is what I said above: nothing directly, but fixed prices is what keeps J1 shps being used, bought and sold. So, IMHO, probably this same J1 ship that keeps this small planet on touch with the Imperium will not even exist without fixed prices, as it would be an obsolete artifact with no advantages.