See your reasoning but I think you are doing what we all do at times; ie bend the figures a bit here and there and then say well it nearly fits.
First of all from an energy point of view
A 12m/s wind contains root 2 (1.41) times 50% (ie difference in linear speed) as an 8m/s one.(ie a 12m/s wind is 50% faster than an 8, so it contains about 70% more power.)(ie x 1.7 )
In 15 knots I would be on around a 6.5 (or even 6.2)
In 25 above figures would give me a 4.2 (ie 6.5/1.7)(for equal power ???)
Which is about correct.(Id be getting overpowered with 4.7 and thinking about 4.2)
This model would also show sailors coming towards similar sized sails as wind gets stronger. (which is one of few facts we have.)
PS Your equation gives me an 8.2 metre in 15 knots ?? and a 5.5 in 25. (Both out, my biggest sail is 7 and I sail from around 13 knots)
It just cant be linear when doubling wind quadruples power ! Its what makes fin and sail choice so interesting.