I consider measurement omission a narrow aspect of a broader issue. Objectivism, on the other hand, presents measurement omission as a huge, broad principle. There's a disagreement there.
When looking at stuff, we always must choose which attributes to pay attention to, because there are infinitely many attributes which are possible to look at. (This idea partly comes from Karl Popper.) We have to find ways to omit or condense some stuff or we'll have too much information to handle. Like Peikoff's principle of the crow, we can only deal with so much at once. So we use techniques like integrating, condensing, omitting, and providing references (like footnotes and links).
Regarding infinite attributes, let's look at a table. A table has infinitely many attributes you can define and could pay attention to. Most of them are dumb and irrelevant. Examples: the number of specks of dust on the table, the number of specks of dust with weight in a certain range, the number of specs of dust with color in a certain range. And just by varying the start and end of those ranges, you can get infinitely many attributes you could measure.
The way we choose to pay attention to some attributes in life, and not others, is not especially about measurement. Some attributes aren't measurements. I think some attributes aren't quantifiable in principle. Some attributes may be quantifiable in the future, but we don't know how to quantify them today. For example, do you feel inspired when looking at a painting? We don't know how to measure inspiration or what units to quantify it in.
Deciding which attributes are relevant to what you're doing requires judgement. While many cases are pretty easy to judge, some cases are more borderline and tricky. How do you judge well? I'm not going to try to explain that right now, I just want to say I don't think omitting measurements answers it overall (the measurement omission stuff definitely does help with some cases).