If you extend this logic then it would imply that government should simply prevent anyone from getting rich - dead or alive. If you were socialist then you still wouldn’t have issue with this but for all others this would be infringement on their right to own property and more broadly to achieve prosperity even while doing nothing illegal. In other words, becoming rich should not be an act of crime that leads to stiff penalties.
A more logical view is to think of inheritance as just usual income to other person and hence eligible for usual income tax as contribution towards shared goal of the society.
1. You can extend that argument like that, but I wouldn't. At least not to "there should be no rich people at all". But at some level of wealth, a difference in quantity (of money owned by an individual) becomes a difference in quality, and IMHO we should think really hard if we want that difference to exist in our societies.
2. I agree that an inheritance can/should be treated just like an income. And that's why I applied the usual tax fairness argument of "the more wealth you have, the more responsibility you bear for financing public services, because you have greatly (if perhaps indirectly) benefited from them."
A more logical view is to think of inheritance as just usual income to other person and hence eligible for usual income tax as contribution towards shared goal of the society.