It leads to the intuition that an economy where 100 people consume 10000 (let's say of energy because it should be inflation-independent) per week and 1 person consumes 100000 is worse than an economy where 100 people consume 9000 per week and 1 person consumes 10000. That is, you can strongly reject or disapprove of changes that strictly increase everyone's wealth or consumption.

I think this is not only mistaken but would wrongly lead people to often oppose economic growth, which is likely to increase inequality at least somewhat in many circumstances, while increasing almost every other measure of welfare. They often point in opposite directions.

The case where inequality is most important is when there are things whose supply is fixed or very inelastic (famously land, maybe housing), in which case you are in more of a long-term competition or bidding war with other people for some of those things. That might be a reason that total consumption is an imperfect metric too, because maybe your consumption of one thing with elastic supply (food?) went way up as the economy grew but your consumption of something with inelastic supply (housing?) went down at the same time.