If so many of the youth of today can't be bothered to register to vote using the current GOV.UK website then why would you think that they suddenly might be eager to register over an app instead, which would require the same level of effort as the website they could (but don't) currently use?
The big benefit would be that, if they can be bothered to register (something many currently don't do) then the actual voting process might be easier rather than going to a polling station. However the problem yet again isn't that voting is too hard currently, it's that lots of people are either happy to go with the flow, just don't care or can't be bothered so developing "an app" costing millions and ensuring it's secure just won't change enough of the non-voters into being voters to make the whole thing worthwhile.