Just done a quick availability check on 5Ls to see which letters are most popular
1st: all 26 letters so it's not exactly CVCVC
2nd: all 5 vowels
3rd: all 21 consonants
4th: only a and i
5th: only s
This gets to 5460 combinations. Then I checked availability for the first 3000 on GoDaddy, in batches of 500, out of 3k about 240 were available for hand reg.
2nd vowel. Doesn't seem like it's that important. Pretty normally distributed, i slightly more popular than u.
u 67
o 46
a 44
e 42
i 41
3rd letter. This is more interesting. See results below.
q 72
y 34
j 25
z 23
h 20
x 18
w 12
f 10
k 8
c 5
b 4
p 3
l 2
v 2
m 1
r 1
d 0
g 0
n 0
s 0
t 0
You should read in reverse order, if many letters are available for hand reg, then it means the letter is not that popular. Q is clearly the least popular. 3rd letter Also - no domains for hand reg are available with d, g, n, s, or t in the middle.
Of course this is assuming 5th letter s, and 4th letters a or i. Otherwise there would be too many results to test. But it's still an indication.