As so often, the answer is a combination of local tradition and economic reality.
Not all self-catering accommodation is per week but a fair percentage is.
Most UK people who travel to the cottages are going for the whole week, the places which rent them out are geared to that and do not want to rent them out for shorter periods as that will result in the cottages standing empty, unpaid, for times that are too short for others to rent them.
Those agencies and parks that often get requests for shorter periods or dates other than the most usual ones will often offer those periods for the higher rate with a lower rate to fill out of the rest of the week, but less than a whole week would cost.
I see something like that in the Netherlands, where the typical holiday park cottage is available for weeks, weekends and midweek periods, with the weekends going at a premium price, and the midweek periods going cheaper as those are used as fillers.
The 'week' periods often change on the Fridays, same as the start of the weekends.
In the UK there is less of a tradition of 'weekend' and 'midweek' rentals, so holiday providers prefer people to rent for the whole of the week. And if you only offer whole weeks, you might trick people in paying for more days than they would like.
Hotels and B&B people are more used to people comming for just one or two days, and the owners know that if they have their accommodation empty for a few days, they might get people to come in on the day itself.
They often still offer lower rates for weeks or ask for minimum periods, to get the most out of the market.
But as with all kinds of accommodation everywhere, ask.
There will be cottages that go empty for weeks on end and the owners might be happy to rent it to you instead.
You may need to go through a search site, go airbnb or call many parks, but I would be surprised if nobody will rent out self-cartered accommodation for less than a week, even when it is advertised as 'full weeks only'.
And as said in the answer by @vclaw for some rentals there are the practical limits of having staff on hand, or even the owner being around at all, during the working week. But there might still be the option to rent part of the week outside the tourist season, as the owner might be happy to get less money rather than no money and might be able to arrange key-collection, payment and check of the property with someone who lives or works near.
