There are several things to consider here:
1. SLCOM was a
Star League organization that controlled the all communications, and everyone was fine with that for quite a period of time. We should not write off some inertia of minds.
2. HPG network was damaged during the Amaris Civil War, at least on Hegemony worlds. ComStar not only controlled, but also restored damaged stations. If ComStar did not exist, Houses would have to do it themselves.
3. The comparison with the SLDF situation is not entirely correct. The leader of SLDF left the Inner Sphere, abandoning forces that refused to accompany him. SLCOMNET did not have such a thing: William Blake did not go anywhere. Moreover, there was a smooth transition from SLCOM to ComStar. For people inside SLCOMNET not much changed (before Toyama and Karpov). Probably, ComStar was the most stable entity in the entire Inner Sphere during the period. Their declared neutrality could have helped. Moreover, ComStar had a reliable source of income. Remnants of the SLDF were a military. How would they earn money, aside from turning mercenaries?
4. How many key personnel does each station have? They could have limited numbers of technicians that were directly related to hyperpulse communications. Thus, ComStar could have fewer people to be really concerned about. Moreover, communication interdiction is not a very surprising idea. Star League could have considered it itself. It probably did not want to abuse such power for political reasons, and Amaris could not interdict anything, since he did not control the entire network.
5. Blake did have a high moral ground. Operation SILVER SHIELD was relatively bloodless. It could be easier to convince ComStar personnel to use interdiction. It's not like it was directly killing people, and considering what the Houses were doing at the time, many probably felt that a short interdiction serves them right.
6. Houses could have used an "I'll think about it tomorrow" approach. Blake was appointed the head of the SLCOMNET during uncertain times, when the war looming. And SILVER SHIELD happened when everyone was already fighting each other. Probably, Houses did want to deal with ComStar at first, but for tactical benefits of not being interdicted immediately the solution was delayed each time until the end of the war. Also, ComStar did keep the word of being neutral. They did manipulate the information during later, but on the most part, they were neutral. Our perspective gives us a view that very few in-universe characters would have. Ironically, Toyama's transformation of ComStar into a secritive order could have saved them.
7.
I mean, it's a fictional universe. If nothing's been written about it, the default assumption should probably be that it didn't happen. Otherwise we're basically talking about Russell's teapot. It could be that Max Liao had five additional battalions of Death Commandos that he disbanded and sent to the copper mines on Brazen Heart because he felt they were more loyal to Pavel Ridzik than him, but since it's never mentioned anywhere in canon, I think we shouldn't assume it to be the case.
Umm... Russell's Teapot argument does not apply to Archangel's reasoning. The problem with Russell's Teapot is not that you assume its
existence, but that you assume existence of a
teapot in outer space. Would one replace a teapot with a rock of a teapot size, the assumption would reasonable (while still being an assumption). What Archangel suggested is a reasonable assumption about how things work. I do not think it should be dismissed on a technicality. It's true that some official explanation would be preferable.