You can just not push optional resources. Or push the smallest responsive asset and let the full-scale one come in if requested. Just because it doesn't handle every edge case doesn't make it a failure. Being able to push required dependencies without a round trip is a huge boon for those same mobile users that might have restricted bandwidth.
If the mobile user already has those resources cached, it ends up using more bandwidth. It's possible implement checks for this, but it can be tricky to get right for all cases.
On the other hand, the browser's HTTP cache is well understood and standardised, and just requires sending the correct response headers (at the cost of the additional round trip).
The spec gives the browser the ability to cancel a push in the case that it already has the resource cached. Testing that was one of the pieces of the linked article, because not all of the browsers implement that yet and have somewhat different behaviors.
