Since they are able to be participate in zellbrigen it is reasonable to think that they are not so eager to use the artillery.
That said there are even the artillery omnimech in clans, so an artillery protomech isn't something gone too far either.
Although protomech CAN use handheld weapons but it's even worse than mech, for a 10% of them is 1.5 tons at most and they are not allowed to use TSM either.
Even for a 15 tons ultraheavy protomech it is barely able to add a clans gauss rifle(12 tons) at its stock body with MP of 1/2 without any armor and no ammunition for the gauss rifle too, so standard artillery isn't their option at all - even the lightest standard artillery, clans Arrow IV, requires 12 tons for the launcher without an ammunition. So BA tube artillery seems to be the only option to begin with.
BA weapons requires about 50~80% of weight than its battlemech counterparts and I remember that protomech equipments uses the same weight with battlemech/CV, so is it good for 1 ton, a double of 500kg for protomech? It would be feasible to only limit it to put as the main gun. Perhaps having up to 2 or 3 as one main gun would be not so bad either, maybe +1 per each 5 tons group, such as 5~9 can have up to 2, and 10+(ultraheavy) can have up to 3 on its main gun, each considered as a single item like as missiles.
For the artillery attacks, it would be not so bad to allowing the point of protomechs to be shoot as the single artillery if they are close enough(perhaps within 3~5 hex of each others?) but is the maximum damage of 45 quite powerful even consider the 5 points cluster damage spread? Maybe can merge the shots up to six tube worth of attacks, as BA can does with theirs, would be good too if the spike damage seems to be too high.
And per TO, remember that the counterbattery fire aims an artillery and if so it attacks the hex the said target occupies, so if two protomechs are shooting while one the same hex the opponent notes that there are two artilleries on the same hex when making counterbattery attack.
So what do you think about this idea for the houserule for allowing BA tube artillery for protomech?