I believe that bigger_cheese is lamenting his or her inability to do numerical sanity checking in other units. (This loss of numerical information is, perhaps, what you meant by saying that the unit-agnostic approach is 'more lax'.)
For example, if I am looking for a force and I get an answer of 1000 lbs, then dimensional analysis tells me that at least I got a force; but, if my intuition tells me only that the actual force is on the order of magnitude of 1000 N, then I don't know whether my actual answer is way too big, way too small, or about right, unless I know how to convert between Newtons and pounds.
Incidentally, while "units of 1" make correct calculations easy, I think that they are a bad idea precisely because they subvert unit checking; it's hard to know just by looking that 1 + 1 is 1 speed of light + 1 light-year, and hence dimensionally inconsistent.
(Even keeping all SI units can miss some important distinctions; for example, nothing about their SI units (inverse time) allows us to distinguish angular frequency (https://en.wikipedia.org/wiki/Angular_frequency) from temporal frequency (https://en.wikipedia.org/wiki/Frequency), and yet much woe accrues to he or she who does not distinguish radians/time from cycles/time!)
For example, if I am looking for a force and I get an answer of 1000 lbs, then dimensional analysis tells me that at least I got a force; but, if my intuition tells me only that the actual force is on the order of magnitude of 1000 N, then I don't know whether my actual answer is way too big, way too small, or about right, unless I know how to convert between Newtons and pounds.
Incidentally, while "units of 1" make correct calculations easy, I think that they are a bad idea precisely because they subvert unit checking; it's hard to know just by looking that 1 + 1 is 1 speed of light + 1 light-year, and hence dimensionally inconsistent.
(Even keeping all SI units can miss some important distinctions; for example, nothing about their SI units (inverse time) allows us to distinguish angular frequency (https://en.wikipedia.org/wiki/Angular_frequency) from temporal frequency (https://en.wikipedia.org/wiki/Frequency), and yet much woe accrues to he or she who does not distinguish radians/time from cycles/time!)