Sadly, while it used to be the case that customer loyalty was valued by companies, I think it has long been the case that they see “customer loyalty” as a big red sign saying “Here is a Mug. jack up his prices, premiums, whatever”, and you have to go back a very long way (many decades) to find times when “loyalty” was valued.
As others have said, inertia labels you as a target. Not by any means just with insurers, but with banks, mobile phone cmpanies, broadband/TV companies and many, many more. In effect, just about anybody that has an automatically renewing payment authorisation, be it credit card, direct debit or whatever. Exceptions (IMHO) are mortgages which are far more heavily contractually bound and regulated (though keep an eagle eye on time-limited “fixed” deals come expiry of the fixed term), and standing orders. But the credit-card annually auto-renewing things are the worst, IMHO, which is why people like insurers and ‘breakdown’ services (which often are just insurers) are so fond of them. Personally, I always notify them immediately any such contract starts that they do NOT have my approval to automatically charge, and that if I don’t renew manually, it is to NOT be renewed, but considered to be cancellation.
That has a downside, of course. Namely, if you don’t keep on top of it you can find yourself without cover, which is their go-to excuse for using it. My response when they say that is that it’s me at risk should that happen and I’ll take the risk. Just don’t forget …. especially for your car insurance as the consequences (no, it’s never happened to me) can be considerable. All it takes is a bit of planning. First, diarise all such renewals with the renewal date and a 30-day advance warning. Just about any computer or mobile phone has that capability and plenty of free software will, too. Be sure to have effective device backup in place, and working. Secondly, I keep a old-style written diary and, once a month, check the next month for up-coming renewals and sort them.
We are our own worst enemies when it comes to inertia, which I prefer to call laziness. I know all about laziness because I’m hugely lazy myself on such things. I am very fond of convenience, but have trained myself to NEVER rely on companies looking out for my interests if I can’t be bothered to look out for my own. There’s been an occassional rare exception where they do, but the vast majority, in my experience, subscribe to the mug-alert pholosophical school of customer inertia.