You're right, there is no difference between the long-short (LS) portfolio between two returns or two excess returns, the risk-free rate cancels out.
But there is an economic reason why we consider returns, excess returns and long-short returns. A simple raw return does not tell you much as you need to incorporate how much it cost you to obtain that performance. If a stock returns 1% but the risk-free rate is 2%, then your real return -1% after considering that you first need to borrow $1 to invest into the stock. So, the raw stock return really doesn't tell you much if you don't subtract the cost of having this return.
The long-short portfolio is different. Here, you gain $1 from selling one portfolio and invest this \$1 into the long portfolio. Hence, people refer to a long-short portfolio as ``zero-cost portfolio'' because you don't need to borrow \$1 at the risk-free rate (the funding cost is covered by the selling of the short portfolio). Equivalently, you can of course gain \$0.5 from selling one portfolio and investing 50 cent in the long portfolio. It doesn't matter.
An example is when you run a simple time series regressions using the Fama-French factors. You never regress the raw returns on the factors, you always first subtract the risk-free rate because this is the true performance an investor would have by investing in this particular portfolio. Similarly, that's why Fama & French subtract the risk-free rate from the market portfolio ... one needs to borrow \$1 to be able to obtain the market return. The other factors, SMB and HML (1993) or CMA, RMW (2015) or UMD (1997) etc. are all long-short portfolios and hence do not include the risk-free rate as they have zero funding cost.
