Can you actually transfer them to your Carrier?
Probably not.
This seems like a relatively easy fix. Once a power has some arbitrary number of strongholds, they would decay without undermining. Same for a much larger arbitrary number of reinforcement systems.
That ends up as a return to the Powerplay 1 "overheads" system, where people doing the things the interface says they
should be doing (acquiring and reinforcing systems for their power) end up hurting the power overall by making it "too large".
It probably also encourages an even greater focus on reinforcing than active undermining - if groups know that they need to budget N merits just to keep systems in their current state, in the complete absence of any attacks, that's N merits they're definitely not spending on actively undermining anyone - without addressing any of the major reasons that there's already a weekly surplus of around 70 million CP reinforcement merits.
- organised groups are generally incredibly risk-averse and tend to see 1-for-1 trades of systems as unfavourable, so will almost always put more effort into defence
- you get to use a lot more of your rank bonuses when reinforcing because they only work in your existing territory
- reinforcement actions tend to be legal and profitable in credits and materials too ... whereas undermining actions tend to be illegal and only give merits
- reinforcement actions are far more "things someone might do anyway" (bounty hunting, profitable trades, hand in exploration data) whereas undermining actions tend to be things you need to deliberately go and do because you're Powerplaying today.
- weekly missions tend to be mostly reinforcement with the occasional acquisition and undermining task
- a lot of the equivalent reinforcement/undermining actions are just plain better in the reinforcement version [1]
- system strength penalty and beyond frontline penalty can cut the effectiveness of an undermining action in half or worse, while reinforcement actions are always carried out at full power
It really depends what Frontier see as the vision for Powerplay:
- if it's supposed to be a territorial competitive wargame, then the undermining/reinforcement balance needs to be neutral or maybe even slightly undermining-heavy so that there are more player-driven fights: it needs to be players directly causing the totals to be equal, based on the incentives and balancing Frontier set out. I don't think there is any easy fix for that - it'd require substantial adjustments to a lot of things.
- if it's supposed to be a polite "first come first served" mostly cooperative way of adding some variety and decorations to the bubble, then the current setup is fine, because Colonisation will provide new systems faster than Powerplay finishes reinforcing them, and even with further substantial delays to Colonisation it'll be ready in time.
[1] For example, Reinforcement gets "profitable trade" which even without the 1t exploit can easily get multiple merits per tonne (and "rares trade" when it was enabled was even more powerful). Undermining gets "bulk flood" which caps at about 1 merit for every four tonnes. Reinforcement gets bounty hunting (tens to hundreds of merits per kill, plus a few extra from scanning the pirates first) while Undermining gets murder for 20 merits a time (plus a bounty and notoriety to slow down how often you can do it).