A lot of generalizations here. I live in the east, I hunt literally out my door on public land--as in, if I wanted to I could arrow a deer FROM my back deck. I hunt public land on no less than 5 or 6 separate parcels of public land, including municipal land, 3 large state parks, 2 WMA's, some random uncategorized fish and wildlife dept land, and some private timber land with deeded public access, totaling north of 50,000 acres, all within 30 minutes of my house. Extend the drive to 1.5 hours, and I have national forest, a pile more state land, and a ton of deeded public access land of various flavors, enough that I could never hope to hunt it all in a lifetime. I generally have a pretty good response to asking for permission, and have a handful of properties where i have permission, but honestly I havent needed to ask that much. I grew up in the Adirondacks, which is a 6,000,000 acre state park, most of which is huntable public land--I can be at my folks place if I wanted to use that as a home base, in 2 hours. I can also put my boat in the water on a 100+mile long lake with one of the best bass fisheries in the country, and fish for trout in a several nearby rivers, all within 30 minutes as well. I am very fortunate to live in a state with crappy hunting so it's not on anyone's radar, and I also have made conscious decisions and sacrifices to live where I do, for better and for worse.
That said, if you look at where MOST people live--i.e. big cities, the coasts--and you look at where the public land is located near where those people are, you will see that it doesn't line up in most cases, especially on the east coast. I completely understand that work, family, etc are important priorities that affect most people's ability to hunt. I also see that if it takes you an hour just to get outside the city, a piece of crowded public land that's 15 miles away might still be a before-dawn-to-dark-thirty outing just to get in a 1/2-day hunt, and that can be hard for people to do on a regular basis. Frankly, if that were my reality I wouldn't hunt, I'd either move or find something else to do that I found rewarding.
There is pretty good survey data on hunting participation out there, I don't have a link handy but last I read through it most of the top reasons people cited for stopping hunting, I interpreted as all being some flavor of "I can't/won't manage what it takes for me to get in good hunting locally". This was anything from "the hunting near me isnt very good", to "there isnt enough near me" to "I dont have time" (which I see as the combination of several factors, i.e. if the hunting was better or closer, or both, people might shift priorities differently), etc. All relevant, because overall, hunter numbers are declining and will continue to do so as the baby-boom generation ages out, because in the big picture those numbers aren't driven by "hunting in the Rockies and West", they are driven by "hunting as done by most people" . Yet numbers of people applying for tags in "the west" is increasing significantly--it's crystal clear this is not becasue hunter numbers are increasing, its because the number of people who want to hunt IN THOSE SPECIFIC PLACES is increasing.
All that said, if you 1) live in the east and can't/wont move, and 2) choose not to hunt in the east for any reason, and 3) find that not being able to hunt out of state every year due to tag allocation is a problem, then you probably need to either learn to like hunting somewhere in the east, or give it up. I'm honestly not sure what other options there are, they aren't exactly growing more land and critters on trees, anywhere.