Generally you are not required to exchange your licence, and you won't benefit much by doing so. If your old licence has still a few years' validity left you might not want to bother. However if it's validity is close to the end date you can only renew it where you are resident. Exchanging the licence will also automatically renew it, so any time you do the exchange you will get a new licence with a new validity (usually 10 years).
However once your old license is nearing it's expiry you have to renew/exchange it in the country where you reside. Note that you should definitely do that before the old one expires to avoid any issues during the exchange. As stated the licence you get back will have a new validity.
One exception to the above is if you are exchanging an EU licence, that you obtained by exchanging a non-EU licence in your previous country. These licenses are not considered real EU driving licenses, and they will only allow you to drive in the UK for a year after entering the country, and you actually have to retake the test to get a full driving license.
One other exception is if you are older than 67 when becoming a resident. In this case your old driving licence is only valid for a maximum of 3 years after becoming a resident, after which you have to exchange it to a UK one.
While insurance costs don't usually change, one huge benefit of having a UK licence is that it is probably the most convenient Proof of Address you can have, which is usually required when doing business with banks and other institutions. Also note gnasher's comment on getting speeding tickets:
If you get a ticket for speeding, red traffic light etc. you can just accept a fine and points in your license without going to court, which is usually a lot cheaper than going to court. That's only available in the UK if you have a UK license.
On the other hand having a UK license will make it much harder to prove that you are not a UK resident in case the police catches you driving a non-UK licensed car in the UK (including if you moved out of the UK and are not in fact a resident, just visiting as a tourist).