No, it should be part of HTML. A dimension or unit tag. It seems like a perfect continuation of semantic tags and the direction of XHTML 2 before the presentation-focused monstrosity that is HTML 5.
Units are harder than you might think. If I write 1 pint do I mean an imperial pint, a US liquid pint, or a US dry pint? The foot is equally tricky.
This requires that the person writing the page gets it right, whereas with plain text we can rely on context to make a good guess at the unit that was meant.
I don't think that's a major issue. It should be straighforward to disambiguate: make separate units for imperial pint, liquid pint, dry pint, etc. If this is cumbersome, provide an option to set aliases for these in a meta tag, for example. If the writer of the document is sophisticated enough to be using these tags, they should be sophisticated enough to look up what the proper name is for the unit they're using.
If I need to pay and the price is in 'Dollar' I assume the recipient can clearly indicate if it's a USD or a AUD that he wants to receive here. Francs and Swiss Francs shared the same name, but were different things (and had different abbreviations).
The same would be possible for the units you mentioned.
A lot of wikis do that (wikipedia for one). Eg {{m|1500}} is 1500m or whatever the user wants to see it as/the website wants to display it as. I find it extremely useful.