In a lot of ways this appointment is an excellent one (particularly as you say in the short term),
I think Pochettino has done brilliantly well at Spurs and has arguably been the best manager in the country for the last 5 years. I now he didn't win anything but what was it, a Champions League Final and 2 2nd places. I mean in another universe it could feasibly have been 2 titles and a CL. Football is very fine margins.
It has gone a bit stale though and feels a bit that it's coming to the end of a process for him though. I also think some of the players have outgrown him and what he is trying to do. I'm not sure if there is enormous appetite, desire or money on Spurs part to want to give him another 3-4 years to essentially re-build another team. In many ways more is the shame. Football on the whole is a bit bizarre on this, that they won't trust a manager who has done very well for 5 years because of a bad 6 months. But thats very much the industry we are in.
There will be some reasonable points to ask well won't Mourinho face similar difficulties. In part yes. However I think he's far happier managing older pro's (and I think he prefers too). I think there will be serious efforts now put into getting Eriksen, Alderweireld, Vertonghen and Rose to sign new deals. I'd also suspect working with Mourinho will be a massive incentive to do so. He can quite easily turn that group into title contenders.
If you think about what he was asking for at united, he wanted two centre backs like Vertonghen and Alderweireld, a left back like Rose and creative player with the profile of an Eriksen. He'd have also loved a striker like Kane. While I don't think there's an awful lot of improvement to be gained from such players, if he can get them back to their best they will be serious contenders.
So yes I think Spurs will have a right go at the league next season. After 3 years I'd suspect you will have problems, but then looking at the age of the squad that was likely always going to be the case.