I'm not trying to justify the rules, and I do recognise that there are possibilities to conceal or obscure misbehaviour. Such situations are very difficult, and the difficulties go beyond the practical, as it is often the case that emotions are heavily invested in these things. If my answer seems hard-hearted, don't hold that against me: I'm trying to explain the rules as I understand them.
The executor is a trusted person, trusted by the testator and trusted by the court to execute the will properly. If a mistake has been made in placing trust in that person, it is very difficult to undo. And, as I indicated earlier, there is little pressure on the executor to account for his/her stewardship. A challenge is possible through the courts, but it can be difficult and expensive to go down that road.
The reason why I say that all assets, including personal papers, are vested in the executor is straightforward: there is no other sensible approach. Property passes through the will, even if that property has little or no commercial value. I would actually take a strong position on personal financial papers: they are more likely to be of use to a conscientious and dutiful executor than to anybody else. I can tell you that in that box of papers to which I referred in an earlier post, I discovered the existence of a valuable life insurance policy of which the family was unaware, found documents that helped me with some small but useful financial claims, and was able to deal with tax matters that had not been finalised.
The sort of conflict of interest that is troubling people who are posting here is almost standard in the case of a lay executor, particularly in the case of the will of an elderly person. People tend to nominate trusted family members as executors, and those family members have often been heavily involved in the testator's affairs prior to death. Being an optimist about human nature, I like to believe that this is a satisfactory arrangement in most families, but being also realistic, I am sure that it sometimes arises that some people take unfair advantage of a position of trust.
Anybody who has serious concerns about the administration of an estate can invoke the law, and ask the court to require the executor to submit accounts (See
http://www.irishstatutebook.ie/1965/en/act/pub/0027/sec0064.html). I'm not too sure how this works because, as a lay executor, I have managed to avoid such issues of distrust. But I'm sure that it is expensive and causes great discord. If you think you need to go down that road, I suggest that you consult a solicitor rather than a lay person like myself.