MM, the main reasons for using Twitter is the fact that it is public and searchable, and not hidden within their website. Them failing to acknowledge it is their own downfall if indeed this were the case.
There is a difference between investigating it and prioritising it for repair. All leaks I have reported have received some kind of attention pretty quickly, and have been publicly acknowledged quickly by @thameswater as Michael's quote shows.
I agree, the outcome and action is not always what we want or expect, but personally I find it handy to be able to snap a picture and tweet it immediately, rather than filling out long forms etc.
I am sure if they were pressed into explaining the prioritising practise, they would give more info why some seemingly 'bad' leaks are left for a long time.