I suspect that when most people talk about inequality, what they mean is, "a few people are doing really good and a lot of people are doing really bad". If you can lessen or remove the "doing really bad" part, whether through UBI or some other means (progressive taxation to fund other programs, whatever your ideology prefers), then statements of inequality start to mean just "a few people are doing really good" and I think there are far fewer people that are bothered by that.
I also think these conversations tend to get stuck on the definition of poverty. Some people say, "well, it can't be poverty because they all have smartphones", and other people say, "well, it's poverty because they lack any opportunity". I think that if these discussions are going to get anywhere we have to start by convincing people that the definition of poverty is allowed to change and that we shouldn't in the 21st century be defining poverty in 19th-century terms.
I'd say the problem with inequality is something else entirely than "some people doing really good" vs "lots of people doing really bad".
It's that there are resources in the world, and some people have way more access to them.
This can hold even when all people are out of poverty: of the potential and resources of the world, still some people could take the lion's share to the exclusion of others, regardless of whether everybody has a house and food on their table.
And this inequality (with the true sense of the word, not mere poverty vs richness) is also related to opportunities and squandered potential (as in: yeah, we all have UBI, but this dumb mega-rich person could pay his way to Harvard, whereas some other with much larger potential -- e.g. smarts, inventiveness, etc-- had to settle for some lesser school, and didn't get as far in their career).
It sounds like you're further to the left of that scale than I am, which is fine, except that it's harder to convince people to the right of me on that scale to move that far left.
Sometimes it's better to suggest small changes.
* inequality subverts the democratic process
* inequality subverts the rule of law
* I'd argue it even threatens human dignity
* in economics, my utility function typically only takes my well-being/wealth/consumption/circumstances into consideration, not my neighbour's. That's a simplification, so that one can do economics. It's pragmatic and expedient - it is certainly neither descriptive nor normative. Although there is a tendency in libertarian/"economism" circles (google James Kwak "economism" if you don't know what it means) and even others (skeptic Michael Shermer, for example) to consider it the rational thing to do.
I don't see why. Yes, if I get 10$ more, and all my neighbours get $10000 more, I will be cranky and unsatisfied, utility function bla bla my ass.
Inequality also depresses human happiness.
TL;DR: excessive inequality jeopardizes democracy, the rule of law, human dignity, peace, and happiness.
In other words, I believe that without penalizing the upper end, too, things will just "adapt" to define a new lower end, if only the only change is to give everybody a little bit of money. To some extent, Germany has been doing something close to UBI for quite a while now ("Grundsicherung", "Harz IV", etc.). It certainly helped prevent that a few people fall into some nasty global minimum with zero income, so its probably better than not having it. But I don't think that only clamping the lower income end alone had a society-transforming impact in Germany.
For instance, I sometimes idly wonder how many fairly sharp and/or self-driven people ended up working for the illegal drug industry vs how society (and those individuals) could have benefited had other paths been available to them. Maybe we've missed out on many exceptional CEOs because they were taken up by the illegal drug industry, became drug lords then somewhere along the line locked up or killed.
Or the looming Automation issue. We may take care of many basic economic activities by automation, and now many people will be out of work - we see that couched as a "jobs" problem, but looked at another way it's and extension that our economic system really doesn't know how to harness human capability. Our current economic system says only give people just enough resources - any excess is pulled away from people who lack leverage (like many who exchange labor for income). And increasingly I think the fact that allocating for leverage != allocating for potential is unbalancing our economy. Now most wealth has accumulated at the top to a very few - and, from world economic growth numbers, that group basically doesn't know how to more productively allocate it on a world-wide scale (or maybe doesn't want to to preserve the accumulated wealth, or some mix).
Massive inequality is driven not by productivity but by compounding debt and other forms of rent-seeking. This always spirals out of control eventually leading to poverty, default or both.
So when we start to hit the limits of growth, one of two things can happen. Either everyone accepts that things are slowing down and agrees to accept less than they were expecting based on the exponential projections, or some people don't accept this and use their political power to change the rules so that they can continue to live according to their expectations, which necessarily comes at the expense of everyone else at that point.
To transition smoothly from a period of exponential growth back to a steady state, or even just sub-exponential growth, -- heck, even to exponential growth with a smaller exponent! -- requires a degree of cooperation that is very difficult to achieve in human societies.
2) Via the same community which invests in roads, schools and (in other countries) hospitals.