This is an exploitative practice which takes advantage of you and punishes your loyalty. Here's the kicker, they're all doing it. You can shop around and maybe get a better deal with someone else but you can be guaranteed in a year or two you'll be facing the same situation. The trouble is, there isn't enough competition in the Irish insurance market to really combat their ability to exploit you. Because it's law, you have to get your motor insurance from a very select group so the threat of you taking your business elsewhere doesn't exactly hold water because someone else will be stepping in to pay the premium you've just declined. It is, even without the intent, a cartel.
It's a never ending merry-go-round that few in government seem willing to put the brakes on. The way I see it, there are three options that those in power could go for.

2. Open up the EU market. We can buy clothes, tech and food from across the EU, why not include insurance in that as well? Insurance costs, particularly motor insurance, are much cheaper on the continent. Simply allowing us to purchase from Spain, Germany etc could be a potential option. The trouble with it? Insurance is a financial product and would require synchronising our financial markets with our EU neighbours. Given the ongoing battle surrounding our corporate tax rate, I can't see our government TDs going anywhere near it.
3. Change the insurance system entirely. This would require a constitutional change and therefore a referendum, but it could be done. We could implement a system of insurance whereby the basic level of insurance (third party) is paid for out of general taxation or a levy on fuel. It would require a governmental insurance department to run it and resolve claim issues etc. In effect a public-owned insurance company. Private companies could offer supplementary products like fully-comp insurance which motorists would no longer be obliged to purchase.

This system would require constitutional change to enact, but it can work if the political will is there.
If you're reading this, I ask a simple favour of you. Please email your local TD, their email address can be found at https://www.whoismytd.com. If you wish, simply forward this article to them and ask that they look it over.