Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious quantity: it is used a measure of the disorder in a system but its units are J/K, which makes it really hard to interpret. The reason why entropy and temperature were defined this way is because they were studied before the athomical composition of matter was completeley accepted. You can read more about this in these posts:
Arieh-Ben Naim, a chemistry from Israel, has really good books in this topic such "Entropy demystified". He is one the main defenders that entropy should be a unitless quantity.
I have always like to understand the gist of things, and the first step to understand a magnitud like entropy is understanding how it can be measured. For instance, I think I know what a speed is because I can reason in terms of space and time. But in entropy, as the way is normally defined, this is hard and tricky, and all the explanations I have heard so far seem to me like quite far-fetched. So here it goes my question. Let's accept for the sake of argument that we are considering entropy a dimensionless quantity. Now we heat a gas, and we calculate the entropy associate to this process. The result would be a number, whatever. Let us say that number is going to be 100. How to interpret this number? What would it be measuring? And finally, do you agree with this vision of temperature units?