Thought-provoking indeed. I agree with you that the scale we've picked for utils is arbitrary, and the zero we've picked is also arbitrary. After reading through the comments, I begin to wonder if we should go farther. We talk about utils as if this is a quantity we can actually measure, but is that true? Are we measuring anything at all? Is a numeric measure of any kind at all helpful here?
Let me propose a situation: Given a choice between beer and steak, John chooses the steak. Given a choice between steak and ice cream, John chooses the ice cream. Given a choice between ice cream and beer, John chooses the beer. Which item has the highest utility to John? There's just no way to make sense of that in terms of real-valued utils because real numbers are transitive, and utility doesn't have to be.
If utils do make sense, I ask someone to produce an actual means of measuring them, fuzzy and approximate thought it may be. I can't figure out any mathematically consistent way to do this that doesn't resolve to some other more easily measured quantity such as money or dopamine levels or quality-adjusted life years (QALYs). And if one of those is what we're measuring, then we should probably just go ahead and say so.
In fact, in different problems we're likely to want different kinds of utility. Sometimes a problem is best understood in terms of money. In others, it's better understood in QALYs, and money may be not the measure but rather the constraint. That is, given that we have X dollars to work with, how can we maximize QALYs?
Bu if we just use abstract "utils" or "utilons" without connecting those to something we can measure in the non-hypothetical world, I'm not sure we get any useful information that applies outside of an axiomatic system that may not model reality.
Given a choice between beer and steak, John chooses the steak. Given a choice between steak and ice cream, John chooses the ice cream. Given a choice between ice cream and beer, John chooses the beer.
Does this really happen? Can money be pumped out? For example, offer John the opportunity to pay $0.05 to upgrade his beer for a steak, then $0.05 to upgrade that to an ice cream cone, then $0.05 to upgrade that to a beer. Run forever. I think if you actually did this you'd find that of the three there actually is one that John would prefer to have.
A common mistake people make with utility functions is taking individual utility numbers as meaningful, and performing operations such as adding them or doubling them. But utility functions are only defined up to positive affine transformation.
Talking about "utils" seems like it would encourage this sort of mistake; it makes it sound like some sort of quantity of stuff, that can be meaningfully added, scaled, etc. Now the use of a unit -- "utils" -- instead of bare real numbers does remind us that the scale we've picked is arbitrary, but it doesn't remind us that the zero we've picked is also arbitrary, and encourages such illegal operations as addition and scaling. It suggests linear, not affine.
But there is a common everyday quantity which we ordinarily measure with an affine scale, and that's temperature. Now, in fact, temperatures really do have an absolute zero (and if you make sufficient use natural units, they have an absolute scale, as well), but generally we measure temperature with scales that were invented before that fact was recognized. And so while we may have Kelvins, we have "degrees Fahrenheit" or "degrees Celsius".
If you've used these scales long enough you recognize that it is meaningless to e.g. add things measured on these scales, or to multiply them by scalars. So I think it would be a helpful cognitive reminder to say something like "degrees utility" instead of "utils", to suggest an affine scale like we use for temperature, rather than a linear scale like we use for length or time or mass.
The analogy isn't entirely perfect, because as I've mentioned above, temperature actually can be measured on a linear scale (and with sufficient use of natural units, an absolute scale); but the point is just to prompt the right style of thinking, and in everyday life we usually think of temperature as an (ordered) affine thing, like utility.
As such I recommend saying "degrees utility" instead of "utils". If there is some other familiar quantity we also tend to use an affine scale for, perhaps an analogy with that could be used instead or as well.