Why dismiss a tool outright? Crits are a simple way to introduce multimodal statistical distributions (along with their natural mirror, the "miss"). The primary advantage to doing so is that it creates more discrete outcomes, which are generally easier for humans to reason about, and counteracts a tendency for longer sequences to converge exclusively on the mean. This can assist in tactical planning and also encourages player to introduce narratives (in the negative case, a malevolent RNG, in the positive case the attribution of heroics/cowardice to units). Rolling on the high end of a normal distribution doesn't tend to create the same excitement/anger as jumping to a different damage region.
Depending on how this one aspect interacts with the rest of the system, it can have a positive, negative or neutral effect on strategy and on gameplay variation. It's just a tool, it can fit well or poorly, be implemented intelligently or haphazardly. The addition of crits doesn't inherently make a game more strategic, it can move the needle either way.
As a game gets longer, the players will all congregate at the mean outcome. One hand of poker is luck, 1,000 are skill. A game involving one attack will be lucky, a game of 1,000 attacks should require skill.
An important detail to keep in mind is that people vary a great deal in risk-aversion or risk-seeking behavior. The risk-averse will focus on the times a crit lost them a battle, the risk-seeking will focus on the times it won them a battle. When designing a game you can target one group or another, try to balance it so both are somewhat satisfied, or provide gameplay options to enhance/mitigate risk (e.g. a class that can't crit and is immune to the effect).