I don't carry a 3 wood, just a driver and a 3 Hybrid. Then a 3-LW. In all honesty, the hybrid is currently in danger of being taken out and replaced with a 2 iron. I don't really miss having a 3 wood in the bag.
With 12 clubs in the bag - adding a 17* as mentioned before is a decent shout. I have a 3w and the thing goes like a bomb off the tee (recent MGC open PPs need not comment however ) but i don't use it off the deck as its deep-faced so the 17* serves its purpose well. The 3w is required on about 5 tee shots at my home course, hence why its a keeper. Why don't you look out to see if sports direct or whoever it was are still stocking the Adams hybrids for next to nowt - it'd be a cheap experiment if you didn't like it and you'd easily shift on.
I carry a 3 wood but don't tend to hit it off the floor unless it's on a bit of a launch pad or sat up in the rough. For the likes of us 20 handicappers and high teens I'd say it's a pretty hard shot to pull off. And not something that many high handicappers can do well or consistently well. So your not on your own. I like my 3 wood for safety off the tee more than anything, so if that's something you think would be a plus then stick one in. But as people say, the one thing that got me down from 20 was getting a much better putting and chipping game. Good luck
In my bag I carry:
Taylormade R11 9.5 Driver - 250 yards
Taylormade Burner 4 Wood - 210 yards
Taylormade Burner 2.0 Irons 6-SW - 175-80 yards
Titleist Vokey 64 degrees - 60 yards
As you can see I dont carry that many clubs. I want to add a 4 iron and a 55 degrees wedge.
I love hitting my 4 wood. Ive got mine in a 16 degrees and cant half connect...however I had the same in a 3 wood and couldnt do anything with it...shape or straight.
I don't carry one, tbh 200 yards out I'm probably not hitting the green, I'd want a club I could comfortably hit to get me up and around the green or put me in a position where I have a comfortable chip. For me that recently was a 5 wood, I've switched to a 4 wood and that has nice distance off the tee and the fairway, the 5 wood was just going a bit high for me.
Easy to use with correct technique and appropriate practice.
Those saying no you don't need one on this thread seem pretty clueless to me. The sort of people who think four wedges is a good idea no doubt. Unconsciously incompetent, modern golfers.