Yes, it is. Lagginess is common regardless of what weapon you're using, but it might well be more noticeable with weapons that fire multiple projectiles (like a shotgun).
I ran a rifle(not sniper)/shotgun combo effectively, but other things were compromised and you end up with quite odd stats. You have to really go to town with the shotgun aspect, concentrating on staggering and crippling effects. If you do that, you can hold mobs off with those effects. I was stunlocking mobs much of the time with my shotgun build. Since all guns in FO76 are made from papier mache and duct tape and shotguns forgot the duct tape, you're going to have to run with Gunsmith on and that's 5 SPECIAL points used solely for not having your guns fall apart so often. When I was running shotgun and rifle build, I didn't use melee. I had a melee weapon on me, but never used it and had absolutely no perks for it. I'm not sure that melee and shotgun could be combined very well. Also, as you've found, plastic is surprisingly an issue with a shotgun build. Shotgun ammo uses a surprisingly high amount of plastic. I'm assuming you're referring to plastic when you say shotgun has ammo issues. If it's lead or steel you're finding an issue, you'll find any ranged build apart from stealth sniper to be be an ammo issue. Most of them use lead and steel more than shotguns do, especially if you go full auto...
...which I did and found it far more fun and effective. I first switched from semi-auto rifle/shotgun to full auto rifle/shotgun, then found that I was using my shotguns less often because a really good full auto rifle can be effective at varying ranges, then decided to try what seemed like the next step on that path - the super heavyweight option if you like. I was using power armour anyway, so I respecced to use heavy weapons. I haven't gone down the usual bloodied route because I don't fancy running around mostly dead all the time. Related to that is the fact that I prefer excavator power armour because of the +100 carry weight (I'm a scavver at heart) and that gives lower resistances than any other PA apart from raider PA (which is pretty bad for PA and not really worth bothering with IMO - may as well remain in unpowered armour until L25 rather than starting with raider PA at L15). I have a full set of modded X-01 that I've never used. I might go for modded T-65 eventually. Or maybe strangler heart PA. Or maybe I'll try unpowered armour for a change, probably with rifles. I have something like 150 spare respec points, so I could give it a try. I fancy running around in civil war formal dress using vampire weapons, just for laughs. An old gentleman vampire.
I probably should change my habits about what I carry. Maybe it's a holdover from the early days when stash space was only 400 so you were forced to carry almost everything with you. I must remember to update the Better Inventory mod to the version that works with Wastelanders. It's one of those "that's how it should have been!" mods. One of the things it does is show the total weight in a stack of items and the total weight in a category of items. I can easily find my aid category creeping up past 150 by itself, then I notice I'm carrying 70 stimpaks, 70 radaways, 50 diluted radaways, etc, etc. I also routinely carry 15-20,000 rounds with me, which is perhaps excessive but it's less total weight than keeping the materials to make that many bullets and keeping a large stock means I have to go farming for ammunition materials less often. One drawback is that I'm keeping alternative weapons and now unpowered armour in my stash. I think I have ~150 units in rifles and shotguns alone. Also lots of materials because I'm still making stuff in bulk just to scrap it to try to learn the last few learnable mods I don't know. It takes a lot of materials to craft thousands of items and you only get some types of materials back when scrapping and never as many as you used even with scrapper card in play.
when you get to that end mission stage where you have to decide if to keep all the Gold yourself or share with the other Faction you did not side with. Share it all equally as it boosts your Reputation a lot for both Factions keeping both friendly towards you as well meaning its a lot easier to gain Reputation Ranks !!