2x2s are an excellent and time-tested storage method for coins. They do have some drawbacks: the edge seal is not perfect on the stapled types, and the self-adhesive types can out-gas solvents from the glue. You have ot be careful of the staples, and not allow stapled 2x2s to scratch each other if stacked together. And, as you've noted, a 2x2 is more bulky than a loose coin, or even a coin in one of those cheap plastic coin album pages.
There are solutions. One old-fashioned solution that might come in handy: a 2x2 is exactly the same size as a standard 20th century photographic slide, so anything designed to hold slides will do a perfectly adequate job of storing coins in 2x2s. Slide boxes are good for bulk storage and now that most people are throwing away their photographic slides and going digital there's lots of slide boxes around on the second-hand market you should be able to get cheaply, but for display purposes, an album page designed to hold photographic slides is what I personally use. Slide album pages have an advantage over the pages they usually sell in coin supplies shops, because the plastics used are generally superior and don't "stick" to the 2x2 film. The 5x4 pages made by Vue-All are what I'm currently using to house the bulk of my coin collection. Vue-All also make "Safe-T-Binders" designed to fit Vue-All's pages, and they work together really well as coin albums; their rigid box-like structure means you can stack them up, without worrying about the albums on top squeezing down and causing problems for the albums on the bottom of the stack.
Last time I bought some last year some time, I noticed that Vue-All have finally realised that their products are good for coins, and have started marketing themselves to coin collectors on their website.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis