Pet owners will gain:
the freedom to travel with pets as they wish (from any approved country), on any ferry (with the consent of the ferry operator) to any UK port, on any airline, with the pet with them in the cabin, if the airline allows (many do for intra-european flights, but are forbidden by DEFRA for flights to UK), or in a private boat or plane. At present, if you want your pet to travel with you (really with you, not as freight or airline baggage), you have to go by car with Eurotunnel (or possibly some ferries, I'm not sure), which can be very inconvenient. Owners's responsibility (apart from the usual veterinary requirements) is simply to declare the animal to customs on arrival, or maybe even, say 24hrs in advance, if arrival is at a little-frequented port of entry.
Everyone else will gain:
(a) there is less incentive for pet owners to smuggle, when they ignore the 'DEFRA approved routes' rules, but more seriously probably also ignore the useful veterinary requirements and import some unpleasant pathogen.
(b) taxpayer no longer funds the make-work-for-ourselves team of DEFRA staff maintaining the 'approved transport routes' list
(c) even UK airports may gain – there are many anecdotes of people flying from e.g. USA to France, and then on via Eurotunnel, becaused DEFRA make it so difficult to come directly to UK.
Losers: As well as the DEFRA approved-routes team, various commercial animal transport businesses and executive jet charter companies will be upset at the possible loss of business from pet owners who with the current rules find it impossible to bring their own pet with them themselves. All these losers will, of course, claim that disaster will ensue for everyone if the restrictions are repealed. As usual, some will lobby, others may do worse to protect their rent-seeking.
Eurotunnel my also lose a bit – from the numbers reported by DEFRA and the number of dogs and cats passing through Eurotunnel's Calais office, it seems almost all pet dogs and cats coming in to the UK come with Eurotunnel. Eurotunnel actually have a very good system, so I am sorry they my loose some business (I don't work for Eurotunnel!).
As a final word, maybe the extra UK veterinary requirements (above the EU standard ones for rabies etc) are also unnecessary. I don't know. But anyway the veterinary requirements are a managable inconvenience, compared with the DEFRA total ban on almost all travel possibilities. So if only one rule is to be junked, it should be the travel route restrictions.