Slide actions are generally the weakest of the various types of repeating, even simply breech loaded, rifles.They have difficulties handling the chamber pressures that a bolt action can, thanks to the basics of the bolt's "locking Lug" design (an issue they share with lever actions).
This has been, to a degree, overcome with modern metallurgy, but the added layer of compexity, the weaker design, the vastly more difficult to clean action and magazine, and the rather unfortunate tendency of weapons with tubular magazines to fail rather spectacularly when loaded with spitzer bullets (and the spitzer bullet shape dramatically improves the performance of a round, especially in the FMJ configuration required under international law) all argue against the pump/slide and/or lever action for a main infantry weapon.
Where the pump could have found a home was as a "sub gun" carbine, chambered for a light, maybe even pistol, round for use by trench clearing troops. In that role the lack of a high powered round, the handiness of the design, and the far faster rate of fire could have been quite useful, at least until someone came up with a true submachine gun.