The real problem is power creep from the CP system. Since it's supposed to give players after lvl50 a sense of progression, I propose the following changes that would address the problem while still serving its original purpose:
1. CPs will make it easier to obtain higher quality gear and comsumables and give various quality of life improvements (give a small chance for looted items to have higher quality than they would have been otherwise including purple->gold improvements, reduce crafting costs, increase the chance to improve gear with tempers, increase gold/AP/Tel Var rewards, increase lockpicking timeout, increase inventory size, increase food buff durations etc).
2. Set the effective limits very high or remove them entirely depending on what makes sense for the respective stat, but...
3. Make it so that the effectiveness of each stat that has a cap increases asymptotically along a fairly flat curve and...
4. Remove the 100 point limit.
5. Increase the cost of respeccing according to the number of points spent (similar to how skill point resets work now) to discourage people from moving around points when they go from crafting to doing dungeons etc.
What this will achieve is:
1. Higher CP players will still feel and be more powerful on average (which is what I assume the CP system was intended for), because they will more quickly be able to get the best gear and consumables.
2. Power creep eliminated forever.
3. The difference in power between new players and veterans will be essentially the same as it is in no CP PvP zones.
4. PvE players will be less reluctant to do battlegrounds, because their builds won't suddenly be out of whack due to lost armor/armor penetration and regen.
5. More consistent game experience.
6. Healthier population in PvP campaigns.
While I enjoy the CP system the way it is now in the PvE context, I avoid no CP campaigns like a plague for the reasons outlined in 4 and 5, and it won't be any different with battlegrounds. But if I was used to a certain power level of my character, going to do some PvP would be significantly less painful. I'm sure there are plenty of other players who feel the same.
And before everyone shouts "hurr durr nerf", obviously the armor skill lines would have to be buffed to pre-Morrowind levels, and possibly even a bit more, but now the devs would only have to balance around level 50 instead of lvl 50 and another level that changes every 3 months, which would make their work easier and our queues shorter.