I'm a rifle and pistol shooter who recently got into archery. To me there's no comparison in terms of cost. There is a slightly higher minimum cost to get started in archery, but ongoing costs? Not even close. An afternoon at the range, not even including the range membership, can run $50-100 even with 22lr ammo these days. Shooting my handloads on average is about $1 per round. Some less, some more. That adds up fast. Having a decent gunsmith do any repair work or modifications will cost WAY more than bow work.
A basic Remington 700, not a high end model, not a bargain model, is almost $1000 just for the rifle. Then you need optics and quality optics tend to start at $500 and go up fast. If I cared about it working on a hunt when I would actually be pissed if I had a scope issue I'd probably start with a Vortex Viper or comparable. You can get cheaper, and they work, but you will see the difference. Just like you can put a $25 sight on a bow but no one's using them on the podium and if you have a hunt go bad because your cheap sight failed... Ongoing ammo costs, replacement stock since the factory ones are usually lousy, sling, safe or lock box to store it, bipod, sandbags... Then you can't shoot it in nearly as many places.
I specifically chose to do archery this year rather than firearms. Not that I don't go to the range now and then, but I wasn't buying any new equipment and I wasn't specifically learning new skills. I'd say I'm money ahead just on ammo saved and have gotten to enjoy a lot more time doing archery than I would have shooting.
One of the real big issues I see is that so many people seem to think they have to buy a high end bow. There are lots of $500-700 options out there. For $1000 you can be nicely setup, something that requires pretty careful shopping to do with a rifle and won't include a few months worth of ammo costs unless you just don't shoot it. About five years ago I put together a 308 rifle specifically for shooting prone at the range. Nothing special, it started with a Savage Model 10T from Cabelas on sale and got a Vortex Viper scope, not a PST model. Bipod, stock pad and a few other minor accessories. My total cost not counting ammo came to just over $1k. The rifle is the equivalent of a walmart or Dick's sporting goods bow, not even one of their higher end models. It's a bargain rifle that happens to be known for accuracy well above its price point. Someone trying to get into archery could buy a Powermax, drop away rest, decent sight, half dozen arrows, basic hip quiver and arrow tube, release... and be shooting in their yard or a local club for the same money
I think the issue is that people have the perception that archery should be cheaper than the same result with a firearm. It's just not and never has been from what I can tell. What's different is where you can use it and your ongoing costs. Gun guys also don't seem to have this feeling that they NEED a new gun every season or two. We might buy one that often, or more, but it's just because we want a new toy or something with a different role. A general duty deer rifle hasn't changed much in almost 100 years. Hell, mine is the one my grandfather used and he got it as a WW2 bring back that was confiscated from a hunting lodge by someone else and the date stamp on the receiver is pre WW1. All he did was remove the rear sight and add a Redfield scope. Exactly as it is would still work quite well for hunting deer almost anywhere in the US. I know guys who use 30-30's and 45-70's with iron sights for spot and stalk who use rifles significantly older than they are because they're BETTER than most available now. Newer doesn't always mean better, just different. If it worked last year and it isn't broken it will work this year.