I see many references to people wanting to "cut the cord", and have an all-mobile home. This is particularly the case in the US, where it is positioned as a sort of aspirational goal by some, while in Europe it is (often) just something that applies to people either living on their own, or who are in lower socio-economic groups.
There's also another big difference. When Americans say "cut the cord", they usually don't mean "cut the cable TV cord as well". They just mean the copper telephone line. But in markets which are ADSL-biased for broadband, that's not a realistic option for most household. Instead, they may be able to use an "unbundled local loop", and keep their fixed broadband, but get rid of their PSTN telephone subscription.
However, with the rise of mobile broadband, many operators' marketing teams are trying to get rid of ADSL connections as well. Obviously in markets with fully-converged operators and quad-play, that's less likely, but for mobile-only operators, they're possibly storing up trouble for the future.
At some point, the operator is possibly going to want to deploy femtocells, WiFi, or some other offload approach - especially if you're a heavy "mobile only" user. And at that point, the lack of an existing broadband connection is going to be a problem.
Not only that, but your copper line will be disconnected at the exchange - and so even if they want to offer you a new fixed+mobile package with a home gateway including a femto, someone has to pay for it to be reconnected and tested. It's even possible that they'll need to send someone to your house to check the wiring still works OK. (When I moved into my current house 2 years ago, I needed an engineer to reconnect everything & install a new socket, before I could get ADSL provisioned).
So for operators, although cord-cutting sounds like a great way to get more fixed-mobile substitution in place, there's a longterm downside with regard to future flexibility for macro network offload.