Q: You say the progression is vi-IV-I-V. Shouldn't it be i-VI-III-♭VII?
A: Technically, yes. If you're claiming that the progression is in a minor key, then it would indeed be correct to start it on the 1. However. It's also not exactly wrong to say that it starts on the 6, either, although that implies a major key for the progression overall.
What's really important about designating it vi-IV-I-V is that not only is that simpler and cleaner, it hammers home the crucial point that the progression is built from the four most basic chords in modern pop music. You take the I, the IV, the V and the vi, and you could generate a huge chunk of pop and rock from the last 50 years. They're versatile enough that you could just switch them around in whatever order; the SFCP is simply one combination. That becomes far less clear if you "correctly" designate it as i-VI-III-♭VII.