Of course those savings aren't actually passed onto the customer but the consumer benefits in other ways. It's about owner ship of trust, if you allow people to keep trusting the comparison websites rather than the actual company offering the service. So it's an antitrust thing. There are more and more middlemen these days and a lot of people don't realise that's what's happening. Facebook for example has monopolised "having friends on the Internet and being able to communicate with them efficiently and en masse" so if you are advertising or selling something better do it there and Facebook can scoop up a share of the profits whereas previously this would go directly to the seller. Google is the gatekeeper for pretty much all information on the Internet so rather than "I know where to find that information" it's "I'll Google it", so to get in front of that queue businesses pay for ads at the top of Google or pay search engine optimisation experts to make sure they are on the front page etc, again more money going to services that aren't the actual service itself.
IF a company refuses to do that then they retain the trust of their users and own that trust rather than deferring it to someone else.
Same reason I try not to use PayPal, if you need to pay something on the Internet now it's "PayPal the only way to pay money safely online" when it is totally safe and free to pay in other ways. In the end it's bad for the consumer because they are given the impression of choice when actually that's a carefully curated marketplace siphoning money off the industry in question where smaller businesses cannot compete with those costs, leading to more monopolies than choices for the consumer. It seems good at first but then it becomes "the no.1 destination" and the invisible gatekeeper of this information is basically just ignored, while making insane profits that should go to new businesses or improving services and often those profits are not taxed in the country where those services are actually rendered (see Facebook, Google, Amazon etc. All the big tech firms paying almost no corporation tax - remember most of the products sold on Amazon aren't stocked by Amazon but by marketplace sellers who are paying for that rather than the product).
People might have thought this would never happen with staying in touch with friends, or finding information. Now all of those multiplicities of ways of doing a thing are put into one place. It's good initially but bad in the long term, so it's a good thing to have options that are not curated by media gatekeepers like that.
Remember Google is the richest tech company in the world (I think overtook Apple recently when merging to form the parent company Alphabet) and 90% of their profits come from advertising in curated experiences they have honed over many many years but in 1995 or so simply didn't exist. That's a LOT of money to come out of nowhere by convincing people "go here to do this thing and don't bother with anything else". Even if the service is good. Except the money hasn't come out of nowhere, it's the same money that would have been put back into businesses and back into jobs and people who pay tax, instead it doesn't benefit society in services rendered or consumer choice or more jobs, it just ends up in other countries or in offshore tax havens where it does nothing except hoarde money for 0.1% richest people. So that money saved by the consumer in some cases costs society a LOT more in the long run and it's part of the problem with the wealth divide. People really should not support such monopolies but in order to get a good deal and get buy on their low incomes they feel forced too... And it all goes round in a circle like that, gradually siphoning money from sensible and responsibly sized businesses (people) and consumers (more people) into corporate hands, all the while those corporations aren't rendering any of the services themselves they are just collecting and presenting them, often with a charge attached for doing so. It's late stage capitalism at it's very finest: maximum profit for minimum effort.