That sounds a bit harsh. That ammo has weight has some influence on the game, but the influence really is not that heavy, as long as you don't go for rockets and rifle grenades, etc. You do not have to walk to merchants all the time, you do not need to go back to your house all the time and get more ammo or switch the weapon, etc. Of course I can only speak for myself, but with around 100 of ammo for a weapon (if it's not a minigun), I can hold out pretty long and if you don't carry every possible weapon and armor with you, there is more than enough room for even more ammo. Especially guns like the Cowboy Repeater, Trail Carbine, Pistols, etc. do not need massive ammounts of ammunition and even if you run out of your favourite ammo, there is plenty of alternative stuff in the gameworld that can keep you running. If you really need more supplies, normally a merchant is close to every quest hub, which can be reached even faster with fast traveling. :>
You just have to clean up your inventory every once in a while and that should be all. Ask yourself if you really have to carry every weapon with you and if you really need a type of each armor and if you really need 2000 leads in your pocket and so on and so on. If you strike out everything you only need every once in a while or just reduce it by half, there should never be a problem with your carry weight in "hardcore"-mode.
Of course, if you have only a STR of less than 4, it will become a problem.