Gunhead, the reason your LE friends urge the 870 upon you is simple. No other shotgun comes close when it comes to reliability and dependability. This is under street conditions, where shotguns rarely get cleaned, lubed, and are subjected to all the detritus and weather there is.
However, most serious shotgunners(Rather than a GOB who shoots a few times a year) maintain the equipment well enough that the advantages of the 870 are not crucial. IOW, if you take proper care of any quality shotgun,it's an incredibly dependable and useful tool.
As to speed, I can traverse fire on 5 targets at 25 yards in 5 seconds with duty 00 and a stock 870 with good hits. Chances are, you could too. I used to get under 4 seconds on occasion. I doubt the best Winchestershooters can cut that time much. Any takers on that?
Remington's Model 17 was the parent of the 37. Ithaca waited until the patents ran out to bring out the 37.The inbetween Remington pump was the Model 31, oft called the "Ball Bearing Corn Shucker".This was a highly machined design like the Model 12 Winchester,and considered its equal. The 31 was dropped in 1949, the 870 was brought out in 1950.The 870 uses more stamped, not machined/costly parts and did so w/o affecting balance, reliability or performance, an engineering tour de force.