Re: M110(A2) 3 rounds for 2 min max, 1 round every 2 minutes sustained. I doubt you'd ever have to worry about the barrel getting too hot when you have to manually load a 200 pound (plus) shell and a hefty separate powder charge on the loading tray prior to hydraulically ramming. You'll wear out the cannoneers far quicker than the cannon.
There's one thing the 8 inch could do that the MLRS and lighter tube artillery couldn't do as well, or at all (other than fire a Hiroshima-sized nuke). This was told to me by Gen. Tommy Franks, U.S. Commander during the Second Gulf War, and was my (1st Cav) Division Artillery Commander when I was a battery commander. Franks said that in anticipation of having to breech defensive fortifications, the U.S. Field Artillery School was concerned that the U.S. military might not possess anything to effectively deal with (Iraqi) trenches and bunkers. This was in the time before widespread use of very expensive precision guided munitions and unitary MLRS warheads. They constructed a series of field fortifications to serve as targets for different weapon systems and proceeded to try and reduce them with 105mm, 155mm and 8 inch howitzers and the MLRS. It was quickly determined that the 105mm and MLRS were completely ineffective. The unguided MLRS lacked the precision, and neither its bomblet submunitions nor the lightweight 34lb 105 HE shell lacked the oomph to penetrate deep enough or displace much dirt on exploding. The 95lb 155mm HE shell did a little better, but it would have taken a heck of a lot of shells to make any headway reducing field fortifications, especially given normal dispersion patterns. You'd run out of ammo first. Only the M110 A2 Howitzer, firing a 200lb or so 8 inch HE projectile had the power and accuracy to defeat the target fortifications with a reasonable expenditure of ammunition.
This test confirmed a lesson learned in WW2 urban warfare, but had been either forgotten or was dismissed as being outdated. This lesson was first learned in Europe, but was later really driven home during house-to-house clearing operations in Manila, during the reconquest of the Philippines. The best weapon to clear dug in troops occupying either field fortifications or resisting from urban structures was the biggest artillery piece firing the largest shell available. The preferred method was to employ a 240mm self propelled howitzer in direct fire mode, with the 8 inch howitzer or gun running as close second choices.