Completely randomly? Definitely no! There are more than 4 million tokens, and if you invested in 99.99% of them you would have lost money! A couple of years ago there was someone who gave up on picking tokens and just bought top 100 listed on Coingecko if I remember correctly. He was doing fine for a while, I don't know if there is an update on that. Anyhow, randomly is a bad idea.
Totally fair- blindly picking from 4M tokens is suicide.

But if you limit “random” to top-trending, active projects with real volume?
At that point, you’re basically doing what most retail does — just without the illusion of control.
Even if you limit, random isn't a reasonable method, you can do "random" in top 100, and it would still be silly move, we have seen plenty of projects be in top 10 and then get out of top 10, let alone top 100, so we know for sure that some of them will go down.
If you do not look at them then you are going to lose a lot more. If you can't do that then you are going to make sure that you are going to lose a ton of money and you won't be really getting a good return. You have to check all of them and if you are careful then you are going to get a lot better results without a doubt. If you do that then you could get a great return because you would be able to get a great return without a doubt. If you do that, then you should be fine.