Overhead costs and spite is the only thing it would give.
The overhead of deciding who is eligible to receive the subsidy is costly. This would be a clear negative.
Lets try to find the positives of just giving it to the poorer households. In other words what financial/economical benefit does it bring? Lets start by seeing where the money comes from. From the state, whom gets it mainly from taxes; but also, albeit in smaller amounts, by printing and devaluating current fiat assets and then some other stuff in even smaller amounts.
Lets look at the biggest piece of the pie, the taxes, and how these taxes are setup. They are set up progressively. Meaning that higher household (medium & high) incomes are paying the higher part of the tax-burden compared to the lower household incomes.
The majority of the amount of money that a lower household income receives through this subsidy is mainly paid by the higher household incomes; Likewise the majority of the money that the the higher household incomes receive through this subsidy are mainly paid by higher household incomes - themselves.
If the state now runs a deficit in their balance sheet, they will have to go where the money is - the higher household incomes and they will tax them some more, the lower household incomes would be left relatively unaffected or at least affected in a much lesser degree.
Isolating this process and looking at the cycle, each time this cycle would happen the poor are getting richer and the rich are getting poorer EVEN if the higher household incomes are not excluded from this subsidy.
To conclude, besides the extra overhead cost of trying to see who is eligible. The fact of being excluded would create a lot of spite, as it feels like another slap for the ones excluded - whom are already contributing more. As now they aren't 'only' paying more taxes, but are also excluded on benefits. It's two tangible negatives over one. Even though they would pay for the bulk of the cost in the long run anyhow and the result would be the same. Two tangible negatives are different feeling than one and creates a bigger negative psychological impact, and as such a bigger negative social impact.
I see you thinking, well the highest incomes avoid taxes. Trust me - this single or select few people don't care getting a few hundred or a few thousand in subsidies. This money is NOTHING to them, nor to the state; compared to the millions of euro the state is missing out on by the many tax loopholes they can use. And even with the loopholes in place, in many cases they still do pay a fair share of absolute taxes; much much more than the average person; much much more than what they will ever get in return from the state or this subsidy, so why make them feel excluded for something so trivial?
One last thing I want to add, what others stated; some medium income and high income households have indeed just no margin left.