Only in the imperial system of measures are mixed units "allowed".
That is, measurements like19 feet 4 inches
17 miles 13 yards 2 feet
5 pounds 7 ounces
3 tons 5 hundredweights 2 stones
etcIn the SI or metric system mixed measures are "not allowed", and they are certainly not necessary. Something like15 metres 78 centimetres 3 millimetresis expressed as15.783 metresand it is so easy with a system which is based on powers of 10. Just a matter of adjusting the decimal point. It can be done on sight, no arithmetic is necessary. Contrast that with trying to do a similar thing in the imperial system.
But do we need to be able to change mixed units into a single unit? Most definitely! Costing depends upon it. So does finding areas and volumes. Using formulas and changing into other systems also require it. So, science, engineering and commerce have to deal with it regularly. It is no wonder that science "went metric" over a 100 year ago.
Perhaps it should be added that, although reference has been made here to the awkward nature of the imperial system, the measuring systems of nearly all other cultures and times have the same underlying fault in their mixed systems
We should be clear where the "fault" lies. It is not in the fact that the imperial system uses measures called feet and inches etc., but in the relationships between those measures.12 inches = 1 foot
3 feet = 1 yard
22 yards = 1 chain
etc.Now consider the measurement of5 yards 2 feet 7 inchesTo change that into a single measure (for whatever purpose) some arithmetic is needed to get any one of these5.8611111 yards
211 inchesIF instead we had10 inches = 1 foot
10 feet = 1 yardthen the above mixed measurement could easily be read off as any of5.27 yards