Is not buying money the worst strategy in Dominion?
I don't know about the biggest - you could buy curses instead - but yes, this is definitely a big mistake and one of the most common.

Buying only silver and gold (aka "big money") is actually a reasonably strong strategy. It's not amazing, it's pretty easy to beat, but it'll tend to win over beginner players and it's definitely way better than buying basically only kingdom cards.

You say you build balanced decks, with a lot of actions. That's not balanced. Money is one of the things that needs to be balanced; you need a decent amount of it along with the actions you get. (You also mention lots of attacks. While those can serve a purpose, making it harder for your opponents to buy provinces doesn't help much if you've already made it really hard for yourself.)

It might help to think a bit about the expected value of cards. Silver or gold in your hand is worth 2 or 3, clearly. An action that draws you three cards, in a deck with basically just copper and actions, is probably going to end up being worth only 1 or maybe 2 coin on average - you'll draw other actions and a little copper. In a deck with a ton of silver and a bit of gold it might be worth say 4 coin on average! And all that silver and gold you've bought is reliably worth 2 and 3 coin on average.

Another thing you can think about is what it'd take to get a province. Stuff your deck with silver and gold, and you'll get one with two gold and a silver, or one gold two silver and a copper; that's something that can happen fairly easily especially if you trash copper and estates. Stuff your deck with actions and you'll probably need a much more perfect combination. How often are you going to get two village-ish cards that give +1 card +2 actions, along with several actions that each give +2 coin?

And finally, silver only costs 3 and gold only costs six. Most of the time, an action that reliably nets you two coin will cost more than 3, especially when you keep in mind you can't play unlimited actions unless you also invest coin and turns and cards buying a lot of actions that grant +actions. Same idea applies to gold. So not only is the silver and gold often worth more to you, but you'll be able to buy it earlier and more frequently than the kingdom cards that'd be worth the same amount. Sure, you'd get there eventually, but the other players who bought silver and gold are going to get the provinces before you do.

So bottom line, yes, ignoring silver and gold is a huge mistake. Buy money - and only buy actions if you think they're better than the money would be.