Many games have critical hits/strikes but have always a ways to influence the chance of occurrence and/or damage associated with it. This is a necessity else there is no point to it. Else will be just the same as changing the damage and introducing luck. Luck is to be evaded at all cost imho in strategy games.
How exactly can the player directly control the critcal hits? Using it only as a second order derived effect would be a shame. Eg for aimed vs auto fire, the decision on the mode to use depend on the conditions and the available and needed TU's, not on the critical strike conditions. Instead of critical damage, one could just introduce a wider variance in the weapons damage to have the same effect.
If you cant influence it directly its probably not on the players mind and thus the player wont mind it happening or not. Unlike rpgs we dont dress up soldiers by calculating the average damage and all other stats to the point exactly.
Quick idea: critical hits could be used to augment second order effect of damage. For example a critical strike will damage the morale by x3 and boost the attackers morale. The victim could be knocked out temporarily or dazed, reducing his TU's.
Control over critical hits is exercised in multiple ways. First of all, the stats your characters which you do have some degree of control over in singleplayer. The extent of this control increases over time as new recruits and stat increasing implants become availible. In multiplayer this control is far greater. Secondly, the weapon used. You have complete control over this. Thirdly, the fire mode, again, you have complete control over this, and consequently are afforded an additional degree of control over crit frequency. Some firemodes, such as the sniper headshot have an almost 100% chance of landing a critical on a successful hit, thus the control afforded by this venue is near absolute in some cases. While there are certainly considerations other than a firemode's critical chance modifier to take into account which will influence one's decisions, it is readily conceivable that the appeal of increased critical rates may tip the scales in decisions between any given number of firemodes. It is a factor like any other to take into account.
Further, merely wider variances would not have the same effect. Higher average damage equal to a percentage increase that is the sum of all crit contributing factors, would, over time, have the same effect approximately.
In any case, the overall impact of criticals on gameplay is minor, unless of course you deliberately maximize your odds of realizing one, in which case, you deserve to benefit from their inclusion. While I agree that in most instances, chance should be avoided and minimized in strategy games, this feature adds an interesting new mechanic to the game that can be strategically utilized and exploited. This specific addition of chance also adds a level of excitement and entertainment that can only be supplied with a randomly determined outcome.
Finally the additional critical hit effects you've proposed are interesting, but I don't find that critical hits should be limited to them, if this is what you're suggesting. If you get hit in a critical area, you're going to suffer for it in terms of health, in addition to whatever other side-effects result.