To be fair, non-simultaneous initiative is not intrinsically broken as a gaming concept. Not having a reaction-fire component doesn't make it better, but it is still a valid core concept. If one wanted to, they could simply house-rule that the Reaction Phase allows for return fire vice simply allowing for BattleTech-style torso twists. But one doesn't need to...because Initiative is rolled for at the beginning of each phase; see below.
I hate to say it, but I think a lot of the naysaying is by people who either never played the rules or simply haven't done so in some time. I will readily admit that I had to pull out the box and peruse it for literally a couple of minutes to refresh my own memory.
In any event, S7 rules are only non-simultaneous if the Expanded Initiative rules (p. 50 of the S7 Gamemasters Book) are in use; and even then Initiative is applied at the start of each individual phase. And a lot of weapons don't have Delays past 1 or 2 anyways (and certain weapons like AC/2s and AMS have 0, just like MGs). There are five range brackets, so while everyone is moaning about the supremacy of the lowly machine gun, it has 12 hexes of range (+5 THM at max), which is a straight-up +0 or +1 THM for nearly very other weapon (excepting the obvious, like Small Lasers).
And the ruleset is *really* tied to MW2 if one wants it to be; more so than I remembered, down to Complex, Simple, and Incidental Actions. They are only 7 pages long, not including the weapons-chart (which only included the 3050ish Inner Sphere/Star League weaponry). And there are more products for it, including the MW's Guide to Solaris VII and of course Map Pack: Solaris VII. Blaine Pardoe and Loren Coleman had a lot to do with the post-boxed set products, if anyone want to look into primary sources (I, personally, do not).
Man, I do miss these rules.