If the original question had instead been about wealth instead of income, one piece of the claim would be vaguely true:
Average wealth per household was $1.1M in 2022. ExcludingThere are around 130m households in the US in total, giving a total wealth of $143 trillion. The 10 wealthiest households reduces this number by approximatelywealthiest individuals have a combined wealth of around $1.2 trillion. So if one excludes them, the average household wealth is around 1% or $10,000 less, but put another waythese $10, there is less than a 1% reduction by excluding000 are presumably the 10 wealthiest householdssame as quoted in the original question.
For comparisonBy similar computations, excluding the 50/1000 wealthiest households reduces the average wealth per household by $25,000/ $40,000. This is not too surprising if one looks at the median wealth per household, which is $141,000 (same source).