Do you think this is always the case? I'm thinking about texas hold 'em, which has short-term variability but the stronger players win over the long run with a better strategy. Does chance have a place in competitive gaming?
A luck element lets players of uneven skill feel engaged. Even better is a great handicapping system like Go has, but that's notoriously hard to design.
Chess is a great game at certain skill levels and has a lot of beauty to it, but games with enough of a skill difference aren't really interesting for either player unless the better player is teaching/mentoring.
So yeah, luck has some place in letting different people (and even gamble) together.
I think that the issue is that people feel cheated if they are in the zone/on a perfect run, and have that pulled from under them by chance. However, I would contest that having some risk makes it more exciting.
Another likely issue is the fear that your tactics and your highly drilled skills might become less relevant if some elements of the game are based on chance/randomized. It essentially negates some of your time investment in the game. For myself, I think that it's more interesting to have to adapt your tactics to new situation. I also find the skills that a game involving chances emphasizes tend away from the repetitive and towards general strategy, for example: map knowledge becomes less important compared to scouting.
For heads-up play (a match between two players), the winrate of a winning player versus a substantially worse player is can be anywhere from 4 big blinds/100 hands to 20 big blinds/100 hands. The standard deviation is more like 140 big blinds/100 hands. This means that you have to play quite a while to have an almost zero chance of winning, even against a substantially worse player. Most professional poker players even have an occasional losing month (let's say one a year an average).