There's two different issues going on with an inheritance. One is being executor/administrator and dealing with the legal side. The other is dealing with the practical side.
If you are the nearest relative and executor/inheritor of a house and "simply refuse the whole deal" then the administration of the estate goes undealt with and the house and contents get left to rot, unless someone else with an interest starts a legal action over it all.
If you deal with the legal side then you are to some extent going to also have to deal with the practical side because 1) you are going to have to search the house for legal and ownership documents to make sure the legal side is properly dealt with and 2) you (if you inherit) are going to be responsible for things like property taxes and utility bills. You could always leave everything else to rot, of course.
If you decide to deal with the practical side as well as the legal side you can get someone else to do the practical side but you still need to find them and agree terms, which is hardly "refusing the whole deal". And even then if you don't do the job of properly employing someone -scoping out the work, understanding the terms of the offer from the contractor, negotiating the deal - then you are not being mustachian.
It used to be the case that most people died owning very little - houses were rented, physical belongings were useful and got parcelled out among relatives, no shares were owned and money in the bank was below the levels at which formal administration of an estate would be needed. Now with more property owned and fewer relatives to deal with it all managing a death is becoming a different scale of problem, and it's one it is not easy to duck out of doing.