I think a lot of the issues brought up here have plagued stats for as long as they've been a tool. Stats are a great tool, and it saddens me when people disregard them so quickly. But, as usual, the problem seems to lie with the questions being asked of the stats.
Using the missed tackles example because it's being brought up: I agree that if you're asking, "Is X a bad defender?" and replying with just the missed tackle count as a stat, then you're not matching the stat with the question, for the reasons already mentioned. However, if you used missed tackles to show that a team overall isn't good at defending, then I think that's matching the right stat to the right question. Obviously, there's more to defending, of course, but it’s a very useful stat to support or disregard a hypothesis. For example, if, over a season, one team had significantly more missed tackles than average, then they’re probably bad at defending. It doesn't tell you why, though. You'd need different stats for that.
Being ultra-critical of stats and whether they answer the question effectively is a great mindset to have, IMO. Knowing what stats you need to answer your question is always 20-40% of the work (depending on how hard it is to get that info). Of course, there are things stats can't answer or provide context for—that could be due to resource limitations or just the way things are. So, yeah, there’s always going to be a massive misuse of stats, just like with any tool. It wouldn’t be such a massive field of study, or as useful as it is, if it weren’t so important.