The wording 'may' is the interesting bit since at no point does it say free traders 'may not'.
{knowing nod}
What gives us the more scope for adventures involving PCs?
Allowing free traders to carry mail.
Agreed.
Of course, they would need to "arm up" first (most stock Free Traders are unarmed when delivered from the shipyard) and put a Gunner (or two) on payroll and reserve 5 tons of their cargo hold before they would be eligible for mail contracts ... so there are some hoops to jump through before meeting eligibility requirements, but those are things that CAN BE DONE.
Also, consider that unlike so many other commodities that can be traded, mail is something that isn't subject to scarcity limits that can push competitors out of the market (per se). It's not like one ship captain can buy up "all the grain" so there's no grain left for the next ship to come along to buy. There is ALWAYS going to be mail to transport and deliver!
Even more to the point, "competition" is always going to be better for the end user (up to a point).
If only one ship was doing mail runs to a star system for a while, having a second ship get a contract to do mail runs doesn't result in a supply/demand crash in the volume of mail getting delivered. If anything, it means that the mail going out and coming in happens faster/more frequently, improving the service. With more mail being carried, more mail will be generated, so as the transport capacity supply side goes up, the demand for the service ought to increase as well ... so it's not like any one ship (or enterprise) can completely corner the market in mail to the exclusion of all challengers/competitors. There is ALWAYS going to be MORE MAIL to transport ... until a saturation point is reached from the perspective of the Postal Union.
Once that saturation point of transport capacity is reached ... THEN the Postal Union can start getting "picky" about who they want to award mail contracts to. Only once mail transport has reach saturation will the Postal Union be able to "pick and choose" the best carriers while weeding out the less efficient/less dedicated starships from their list of contractors. So only AFTER the saturation point has been reached will competition become an issue for the suppliers of the mail transport services (pushing them towards increasing efficiencies to retain their mail contracts) while that same competition works in favor of the demand side of the equation fostering higher standards and better/faster services for mail transport.
In other words, places that are already "over served" with mail delivery contracts may be hard markets to break into as an independent operator ... while places that are "under served" such as backwater regions with little to no merchant traffic may be in a position of "beggars can't be choosers" where they'll sign a mail contract with almost anyone who will keep visiting their world (since almost no one else will) and can meet the absolute bare minimum requirements.
In other words, there is plenty of room for nuance and variety to be found when you Read Between The Lines in an attempt to discern the SPIRIT of the rules ... rather than merely stopping at the LETTERS of the rules and refuse to look any further.