I work every day on DC lines in a really quite busy area of London and the South East. Bar a couple of very specific high-profile incidents caused at least in part by maintenance failings, I cannot think of a single time when a problem caused by everyday failings by or interference from the DC system caused anything like the inconvenience of a dewirement or dewirement precautions for passenger journeys, or for that matter freight. Even the recent issue at Gatwick, something which was something of a complex scenario in an especially awkward location, still allowed 4 out of 7 discrete lines to remain open and fully functional beyond the initial incident being dealt with by the signaller; something which, with the best will in the world, would quite possibly not be remotely viable under many currently-operational OHLE electrification schemes, especially those not of new construction (of which, of course, the 3rd rail system via Gatwick Platforms 1/2/3 isn't). If we look at minor delays due to issues such as track circuit faults, often these delays may impact an initial service badly, but thereafter only a couple of minutes may be lost, depending on linespeeds, calling patterns, signal section lengths and local operating instructions. I have been on lines where only 2 or 3mins were being lost per train due to a signalling problem which later turned out to be partly due to DC electrification, over the course of several hours; in the event of AC system damage, the whole line or at least that section of contact wire would have been out of use for that duration, closing a major commuter route for the whole evening peak. The most problematic signalling issues I come across are 90% of the time those actually found on diesel-only, non-electrified routes...
Indeed, one could argue that, though horrendously inconvenient at times mainly in terms of locations and poor timing, if the DC electrification system almost "self-tests" through the surrounding infrastructure, it all remains far safer to approach during troubleshooting - one only needs to keep a matter of centimetres, rather than multiple metres, away from much DC equipment found "on the ground", unlike AC which requires cumbersome equipment and procedures to so much as approach (which is not to deny both systems have their inherent dangers, of which I am fully aware). In addition, the third-rail system is not prone to having to be rebuilt after damage from poor weather conditions; only the most severe incidents of poor weather will result in third-rail equipment at the scene of an incident being damaged, normally flooding where trains could not run anyway, or icing sufficient not just to cause arcing but also terrible adhesion.
As for your "fizzy drinks cans" comment, I raise you footballs, stray stuff from people's washing lines, balloons, pigeons... you try OHLE on the London Bridge - East Croydon routes and see how you get on...