Sorry, but that is passing along an 'Old Wive's Tale'
Sorry but there must be a million old wives out there that say their .220 burned up the barrel quickly. Any round that travels 4000 fps is subject to burn up barrels friend. That's just a fact. It's a well documented fact at that. All that heat you talk about it generating is not going to leave steel unfazed unless you have a varmint barrel that's about 2" thick. Heat warps things. A slight warp in a barrel shooting ammo that fast and you soon have barrel erosion. There's a reason that "old wive's tale" got started.
I did a lot of research when I was about to buy my .223 and I checked out .220's .22-250's and .222's at the same time. I saw a whole lot of reports of .220's burning up quickly. Considering the sources I checked I'll believe them. It is true that a good aftermarket barrel will last longer than earlier barrels lasted but most rifles don't have those modern aftermarket barrels. And even the good barrels can still go quickly if they aren't perfectly cut and with all the rush to produce we've seen in the past few years I will still be convinced excessive barrel wear is a big possibility with any round going 4000 fps or more and that includes .204's and .223 WSSM not to mention several magnum rounds that also fit in that category. There's a reason we don't see 5000 fps cartridges. Barrel wear is a big part of that reason.
So if you want a rifle that you can't shoot more than a few rounds at a time the .220 might work well for you. What I don't understand is why people consider it a great varmint round when you can't shoot it more than a few rounds without extreme heat issues. You can get yourself a .223 and learn to hold over your target a few inches and shoot all day without damaging your barrel at least in a bolt action rifle. You might warp a pencil barrel on an AR but you won't warp a varmint barrel, bolt action rifle. And it's warping that leads to damage. People say you should never shoot a barrel that's too hot to touch. How many rounds does it take to get there with a .220 cartridge going 3800 fps or more? 5 rounds? To me that's a rifle that's not going to last a long time because I won't buy a rifle I can't shoot any more than that. I've sat an fed my .223 Savage 50 rounds as fast as I could feed, aim and fire. I generally let it cool after 50 rounds. Not 5. And my rifle will still shoot 2" groups at a quarter of a mile. I don't think a Swift would survive that kind of treatment.
I didn't even mention the price and availability of the .220 round (well I guess I have now). Plus there just aren't a lot of rifles chambered for it these days. Did you ever stop to wonder why?
If nothing will do except the fastest cartridge on earth then I can see getting a .220. I thought about buying one for that very reason. But I found a whole lot of reasons not to buy one.