My misunderstanding as the notation you used was for availability. How am I supposed to know you mean damage if you are using a different notation? Also, if you look in SR4A, you will see that bows have an availability of 2 times the rating of the bow, rather than a flat 2 as you posted. So to get even a rating 7 or 8 bow would indeed require the restricted gear quality at character creation.
If want to uncap the damage go for it. It isn't likely to do much more than start an arms race though I will point out that comparing bows, which are resisted by the lower (and many times much lower) impact armour, with guns isn't really worth while. They each have a purpose.
In the future try asking your question in such a manner that it is easy to understand what you are actually asking. It avoids these sort of situations.
You cannot, even with Restricted Gear, get a rating 7+ bow, or anything else at all, at character creation. And incredibly enough, no they actually don't.
Collapsible Bow (STR Min. + 1)P — 4R Rating x 125¥
Bow (STR Min +2)P — 2 Rating x 100¥
The Errata doesn't change that anywhere. Neither bow has an availability of Rating x2, not that it matters because there is a hardcap on the max rating of gear purchased at character creation.
All gear is subject to gamemaster approval—just because you can
purchase something doesn’t mean you should be allowed to get it at
the start of the game. Finally,
no piece of gear purchased at character
creation can have a rating higher than 6 or an Availability higher than
12 (for more information, see Availability & Buying Gear, p. 312).
I also can't seem to find where it actually says what armor that Bows/Other Projectile Weapons are resisted with Impact, meanwhile I have found the table on page 151 SR4AA which says this:
Ballistic ProjectilesBow 0–STR To STR x 10 To STR x 30 To STR x 60
Light Crossbow 0–6 7–24 25–60 61–120
Medium Crossbow 0–9 10–36 37–90 91–150
Heavy Crossbow 0–15 16–45 46–120 121–180