When I was tutoring, i had a few elementary-school aged kids. They'd have homework where they had to do the problems three or so different ways, using each of the methods that they were taught (one of which was always the way I was taught when I was their age). I actually feel like I learned a lot from them, as there were some interesting tricks that I didn't know before helping with the homework. I think that's a really good way to approach it, because a kid may struggle with some of the methods but generally was able to "get it" with one of them, and which method was "the best" was entirely dependent on the kid. For me, being able to see which methods clicked and which ones didn't helped me be more effective as a tutor, too, since it showed me a bit more about how their individual little brains were working.
But I agree, if you're not also at least trying to explain why the different methods get you the same answer, it can lead to problems down the line. Some of them saw the "why" for themselves after enough time working at it, and some needed a bit more external guidance (which, considering they were coming to me for tuturoing, I guess they weren't getting at school). My argument would be that no one really taught me "why" when I was in school learning The One Way to do math either. I still had to figure out little tricks that worked for me on my own, since my brain is kinda weird. It may not have taken me so long to believe that i'm actually pretty damn good at math if I'd done those kids' homework when I was their age, as i would have had more tools in the toolbox to draw from.
Yes, i do think the biggest problem is shoving so many different tricks at them at once that it leads to confusion. There was also a bit of frustration from some of my tutees from having to solve the same problems multiple times. Some found it boring and tedious, and some found it confusing and made them less confident in their skills since not all methods they were taught "clicked".