As one of The Information's sources noted, building its own ISP would allow Amazon to bundle internet service with Prime streaming video (and the rest of the Prime perks, of course), effectively making it a cable operator in Europe. Alphabet may have hit some snags with the rollout of its own Google Fiber broadband service here in the states, but regulations in countries like the UK or Germany actually make it easier for upstart broadband providers to get into the game in those countries without having to build out their own network. Most broadband providers in the US restrict access to their network, but in the UK, for example, BT is required to offer wholesale access to its network. If Amazon were to re-sell that access, it could do so at cost and improve its margins through the retail business or by selling access to additional cable channels like Starz and Showtime, as it does in the US.
While that all bodes well for a Amazon Broadband service in Europe, it's unlikely that the company would try the same strategy in the US anytime soon. Stateside, the FCC does not require providers to sell access to their networks and the lobbyists that have been keeping our cable boxes in the dark ages would probably raise a stink if they were required to open up their networks.