There are many times not keeping units consistent actually does make sense, depending on the scale of things. If you are working in academia, yes please keep the units the same, but in some instances that can be just as big an obstacle to a quick conceptual understanding as using the different units normally would. For example, if I'm comparing the distance 2 football players ran with the ball over a season, I could compare them like this:
Player A ran the ball 17 miles, while player B ran the ball 1 foot (he was benched most the season or something)
These are 2 units of measurement that everyone is familiar with. It is very easy to picture and understand this. However if you are going to be a stickler for keeping units the same, then you'd say:
Player A ran 17 miles, player B ran 0.000189 miles
This is obviously completely asinine. You could try feet instead:
Player A ran 89,760 feet, player B ran 1 foot
Ok, this is a little better, it is easy to compare them and see player A ran much further, but it's difficult to visualize how far 89,760 feet actually is because no one deals with feet on that scale. Listing one in miles and one in feet makes it easier to visualize each actual distance, and better contrast them, and I would do that 100% of the time.
Anyways, I don't think that really applies here, just pointing out that you shouln'td always just use the same units all the time, it really depends both on the data and your audience.
Your centimeter and inch comparison is not really analogous either. A gram is literally defined in relation to a kilogram. A centimeter and an inch are not only defined completely independently of each other, but are part of completely separate measurement systems. Yes, a gram and kilogram are not literally the same unit but they are very easily interchangeable with a stupidly simple 'conversion'. I don't think it's really a big deal to use them to compare 2 things 'inconsistently' in an informal setting.