Are you really under the impression that the Inquisitor is literally going to make his acolytes pay for their own weaponry and equipment? Any sensible Inquisitor will give his acolytes the gear they can use best and be trusted with.
I run my games by a mixture of direct purchase and requisition - but I definitely use the listed incomes as a benchmark of the kind of resources the Acolytes should have available to them.

By the time you reach Scholar Arcanum, you have likely proven worthy of heavy weapon clearance.
Again, look to the background. In the tabletop game, you can field Primaris Psykers, and they don't have heavy weapons options. Psykers are not expected to lug heavy weapons about, and a psyker asking for a heavy weapon of that calibre would raise the Inquisitor's eyebrows right off his face. Lascannons in particular, and other weapons of that stripe, are precious technological gems in the 40K setting: they should be issued only to heavy weapons specialists who are taking on the kinds of target that require them, not as personal sidearms for psykers working as sleuths for the Inquisition. This is confirmed in the crunch by their Very Rare availability.

As a DH GM, I certainly would not consider access to a man-portable lascannon - or in fact any heavy weapon, barring a heavy stubber - a given for a psyker at rank 7. In fact I would think it was pretty implausible. You may disagree, but I don't think my view is too peculiar among DH GMs.

The Guardsman is your personal mule, nothing more; why do you need to use your powers creatively in battle when you can use them to instantly level your opponent instead?
Because that is not the viewpoint from which these assessments are made. From the point of view of anyone who is not a melee specialist, it makes sense for them to carry the group's only lascannon if they want to maximise their individual killing power, but that is not the same as maximising the group's combat potential, which is what the Inquisitor is concerned with.

On top of that, the Inquisitor is played by the GM, and any GM who regards the Guardsman as "the psyker's personal mule" is ruining the game for the Guardsman player and thus a pretty poor GM.

No, it proves that you can uniquely one shot virtually any DH enemy without any possibility of missing, dodging or evasion because you're a Psyker using Divine Shot.
This is a blind assertion that simply means nothing without the context of the improbable appearance of a high-powered heavy weapon.

You are in a 10 by 10 metre room with a genestealer. You have a stub pistol, and Divine Shot. One shot him.

Not at all; boosting your TB + SB total to 8 by Scholar Arcanum (assuming average 31 scores in each) is extremely doable. Second, you can use Precision Telekinesis to Test WP in order to temporarily increase your effective carrying capacity.
But I looked at the sheet you put up above and you hadn't done so, meaning you'd have to trade off some of those other goodies to get it (not to mention Specialist Weapon Training - Heavy (Las), which isn't even on your advance scheme).

Telekinesis-ing the weapon around is a good solution, sure, but it does require the constant sustaining of a psychic power. I know that sustaining powers is fairly low-risk but if you're having to use it for something as mundane as carrying your equipment then it is something of a vulnerability. Not to mention the fact that presumably you are carrying things besides the lascannon, upping the weight even further.

Finally, as stated, you can use a mere Lesser Power to hover out of reach of the Arco-flaggants (they can't deal with this; they're literally raging retards with chainaxes) and kill them at your leisure.
I'm not contesting that: the rest of your argument I don't necessarily disagree with, it's just the egregious image of a psyker heavy weapons specialist that rubs me up the wrong way.