I think TI probably copied that from the HP 48, which used more or less the same syntax. The only difference is that the calculation you show would not have been automatically reduced to _N, but you could use the CONVERT or UFACT commands to get Newtons from kg*m/s^2.
In practice, HP's UI made it a lot easier to manipulate quantities tagged with units: hitting the softkey for a unit would multiply the current value by that unit, and using the two shift keys you could either divide by that unit or convert to that unit. If you made a custom menu to put the handful of units relevant to your current problem domain all close at hand, you would need very few extra keystrokes compared with calculating without using the units system. That ease of use is vital; opt-in type safety should be as easy to use as possible, so that users aren't tempted to fall back to the simpler, less safe method.
In practice, HP's UI made it a lot easier to manipulate quantities tagged with units: hitting the softkey for a unit would multiply the current value by that unit, and using the two shift keys you could either divide by that unit or convert to that unit. If you made a custom menu to put the handful of units relevant to your current problem domain all close at hand, you would need very few extra keystrokes compared with calculating without using the units system. That ease of use is vital; opt-in type safety should be as easy to use as possible, so that users aren't tempted to fall back to the simpler, less safe method.