Definitely not. While I see your argument (that the railway has still provided a service, even if it was grossly substandard), the current compensation scheme is far too lenient and claim rates are far too low (due to difficult claims mechanisms, small payouts and lack of publicity from some TOCs) for it to be an incentive to run a reliable service. It's often the case that a delayed train (assuming the delay is caused by NR or another operator) is more profitable than an on-time service, since TOCs get "delay minutes" payments well before passenger compensation kicks in and the aforementioned low claim rates even if it is late enough for passengers to claim. That's utterly perverse. Running a train late (or cancelling it) should have a definite financial impact; TOCs only care about money.
I'd go completely the other way, make compensation positively punative. Something like 25% of the fare for every 15 minutes of delay with a cap of 300% or £300 (whichever is the greater) would at least make TOCs think.
If tickets were encoded with unique computer-readable identifiers (e.g. using barcodes or smartcards; if the Glasgow Subway can issue their £1.60 single fares on disposable smartcards, there's no reason why National Rail can't use them), then compensation could be completely automatic for all passengers (tickets scanned by the conductor or a fixed "pad" on board the train, meaning the exact trains used by all passengers are known) who paid on card. Passengers paying cash should be able to collect their compensation from any staffed station (or even potentially TVMs); if the railway can manage to have a system that ensures the correct TOC(s) are credited when a ticket is bought, there's no excuse for not having a system to handle refunds and compensation similarly. Unclaimed compensation (i.e. ticket is known to have been on the service, paid cash but no claim made) would be forfieted to the DfT so there is no incentive to minimise claims.
The only time compensation should have to be "applied for" is when the first train of a journey is cancelled and the passenger boarded at an ubarriered station and had no reservation. Even then, there's no reason why that could not be done simply at a ticket office.
Once you have a system where you know exactly (or nearly exactly) where each ticket was used, the ancient (while it was a good step forward in the 1980s, by today's standards it's based on a laughably simplistic model of passenger behavour and was never intended to deal with genuine competition between operators), unfit-for-purpose system known as "ORCATS" can finally be replaced and TOCs can recieve the exact correct amount of revenue for the passengers they carry. Revenue from tickets that aren't scanned for whatever reason (very short journeys, train too crowded for conductor to get through, etc.) can be aportioned proportionately based on those that are and the service levels at the relevant time.
