Somewhere I've got a broken Canon lens cap.... 72mm. There's a scratch or two on the lens hood too (which was reversed for storage at the time), but that's easily replaced.The lens they were on on is fine. There was no filter under the cap, either.
No, I wouldn't leave lenses in my bag without caps. But I also don't put silly "protection" filters on them and leave them there all the time (I do use good quality UV filters in situations where they might actually do some good... shooting sand storms, mud wrestling, motocross races, paintball, etc.)
The coatings on a damaged lens element aren't practical to repair... it required removing all the old coatings and then reapplying equally good new coatings (that's done with a vapor process). It would probably cost more than replacing the entire lens, to have done. And there's a high failure rate anyway, disassembling cemented lens groups and polishing off old coatings. Any actual scratch in the glass itself would not be possible to polish out, that would change the precision shape of the element and ruin the lens.
Canon would simply replace the whole front element (or group). Now, some Canon lenses have plain "protective" front elements, for lower cost replacement. Unfortunately, the 70-200/2.8 II is not one of those. Looking at the lens diagram I can't tell if the front one is a single element that can be replaced separately, or if it's part of a group of elements. If it's just the single element, the replacement might be a little less expensive even though it's an optically complex piece of glass. Canon might be able to quote on the phone or by email. Or look for a local repair shop and have them do it.
If you don't have it fixe, you likely won't see much effect from that damaged coating. It may cause some flare in certain situations, but other than that will largely disappear.