There are obviously arguments for doing so Vim. However what really concerns me is the giving of rights to the dead in a secular society! It is from this problematic that the argument for heavy or total inheritance tax arises. From there follows the idea that there will be large sums of money which come into the control of government (which obviously you dislike)- and how best to dispose of such funds. I was merely giving a Vim-friendly example of what might be done. Given that in our little thought experiment the second chap is entirely lazy and takes no active role in managing his inherited capital, merely presumably handing it over to a third party investment organization to take care of it, I fail to see what the issue is here-> asides from the fact that you would view this as putting too much power in the hands of the state. Although if the state themselves merely collected the money and directly handed it over to external investment houses, and funnelled all dividends and interest accruing from such activities back into the same funds (on the basis that they invest in the UK, and as such this kind of process would benefit the whole of society)... I fail to see how this is massively objectionable in comparison to merely allowing the lazy individual to do pretty much the same thing.
We might say that if the money was earned by the indolent gentleman himself whilst he himself was living, then he has a right to do with it as he wishes... but that once he becomes deceased he loses any right to determine what occurs with wealth accumulated in his lifetime as he no longer exists as a legal entity... and his wishes, becoming null and void as his self-hood does, cannot be prioritized over the well being of all (ie- both to maximise the potential for the wealth to do good in society, and to prevent unearned advantage building up, in so doing encouraging everyone to earn their wealth within their own lifetimes- although of course as you have said there remain other forms of undeserved advantage)
