I've been mulling this over.
I spent a couple of years as a lab technician at a college. I was a graduate Physicist and had also studied Chemistry at school and did electronics as a hobby. I was able to cover those aspects of the job with some flair. I also had to cover Biology for which I had no qualification and only the broad level of knowledge imparted in a general science class when I was 10. In Traveller terms I had Science 0 in biology (but frankly even that is an overestimate).
I was however fully capable however after very little training able to make and safely dispose of petri-dishes, catalogue and identify the various biological indicator solutions, prepare specimens etc. When I was called on to do something outside my expertise I either asked someone to show me (and I learned it by rote) or I looked it up in a book and actually learned it. Sometimes I made mistakes and sometimes those mistakes were beneficial and I gained kudos, and sometimes they were detrimental and I had to fess up. It was however a job and people understood that for the wages they were paying, they weren't going to get fully trained scientist in all those fields.
So my Profession(Lab Technician) neither granted nor actually required me to have any skill in Biology. Having skills in Physics and Chemistry probably helped me to secure the job, but I could probably have conducted the majority of the work with basic instruction like I did for the Biology side. Probably Science 0 in traveller terms. In most of my paying jobs, I have received less than two weeks real training, the rest was picked up on the job and incrementally acquired.
Consider also a professional soldier (here I am talking basic troops, not special forces). Most of us might consider being a good shot to be a primary requirement but this is not necessarily the case. Many soldiers will never fire their gun in combat and even of they do statistics show most shots will not hit their target. Engagements where thousands of rounds were expended often show tens of casualties. This is fine, a lot of the time you are firing to keep their heads down, while your mates get round the side to get a better angle. Some soldiers in administrative roles might be very poor shots as they are not expected to actually engage the enemy. Training is expensive and the most important thing is not to get somebody killed during training so weapon safety is often emphasised vs the ability to hit the target. Marksmanship standards are often not that exacting, firepower in the general direction of the enemy is often more useful than sniping. Many soldiers I have spoken to admit that once rounds are pinging off your Sangar you have to be highly motivated to stick your head up into it so most didn't (and are still alive at the end of it). In Traveller terms, given time to aim, with a decent rifle and a target 400 yards away even with the -3 penalty for no skill, a person with average dexterity should be able to hit a man sized target fairly frequently. Probably not much below the marksmanship standard for the basic soldier.
A reservist soldier will spend more time practicing cleaning their weapon than firing it and more time than that marching about, conducting general fitness, cleaning, digging trenches, and learning melee combat, field craft and these days probably law. They are still professional soldiers but maybe Profession(Soldier) 1.
So my proposal. Profession does not grant any specific skill. If you can convince the referee that the task might reasonably encompassed by the job description then at best you can apply the Profession Skill level as a mitigation against the normal -3 for an unskilled. If you have the skill then you use the Skill level instead, the Profession Skill does not help. In this way Profession skill is a limited sort of Jack Of Trades skill. You still apply the full skill level on the test to make income for the Profession.
This contradicts the guidance in the Robot handbook regarding the Profession(Robotics) vs Science(Robotics) but I am not happy with Profession being a panacea. Robotics is a pretty tight field, but other Professions are more nebulous (Belter is good example). Rules as written are that all the Profession allows is for you to make money practising it. If anything it is used to substitute in tasks where no particular Skill is appropriate. The sidebar on P114 of the Robot Handbook seems to contradict the guidance in the main rules and in the Companion.
EDIT:
Oh yes, the REASON I was exploring Profession so much is because Profession(Labourer) 2 is such a bargain for the Basic Brain. Now I was considering Profession(X) 2 as the basic for a lot of basic utility droids for my Space Port commercial concourse (see I got it back on topic). Now for simple revenue generation engines this works wonderfully since the Profession Skill generates income without lots of complicated supply and demands maths (but I'll be applying the Passenger Availability modifiers).
This led me to query what other professions a basic droid might perform and I considered Soldier. I am thinking Star Wars Battle Droid level of competence here. Suitable for suppressing civilian populations and throwing en-mass into battle, but easily outsmarted (unless led by a competent commander) and with limited initiative. Clearly the ability to reliably hit targets with a weapon is not a pre-requisite

as if you roll 1000 2d6 you will still get plenty of 12's.
These would make ideal mooks to field against Travellers. A credible opposition to say a small planetary militia who might need some specialists to deal with the threat. A cheap army for a medium level antagonist easily replaced if they players decide to waste time shopping (as they are want to do). They are also implacably loyal (if dumb) and so cannot be subverted (though they may be outwitted).
My group will probably be played by children so they need something non-human as an enemy as well so they can "Scrap the clankers" without me having to worry about turning them into psychopaths

I am also having a tough job convincing them to play 40 year old veterans so they may well only have had basic training in their careers.