Oh well, time to get to work on a Traveller - Eclipse Phase crossover.
This kind of personality transfer technology will transform the Traveller setting into something barely recognizable.
However, change is commonly accepted as a good thing. New ideas from fresh minds are essential to keep a business from stagnating. Although nobles may be able to live for quite some time, there is strong social encouragement to prevent any one of them from ruling a family for too long. Liberal families understand the need to avoid the conservatism and infighting that power-mongering brings; the younger generations need to be given their chance. In darker families such power-mongering is kept in check by ambitious duels (in more open families) or dark corridor stabbings (in more poisonous families). Such infighting may be amongst the younger generations
only, acting as a method of 'weeding out' before they can attain power. Alternatively, it may be between young and old; the young seeking to 'create' job vacancies for themselves!
I know this is canon from T4, but it's really just handwaving why geriatric oligarchs don't control everything. People who've spent their lives gaining power by fair means or foul aren't just going to give it up because change is good, the younger generation deserves a chance, or because they're stupid enough to accept a duel, allow lax security procedures, or not stomp out threats with ruthless efficiency. People stick with what works, especially where money and power are concerned. Change is uncertainty. The younger generation can serve faithfully, go found their own empire, or get stomped into dust like all the upstarts before them.
With personality transfers, there would be a fundamental disconnect between the people who have access to the technology and those who don't. Those who know an avatar of themselves will live on possibly for centuries will have a vastly different perspective than a person who sees life as growing up, getting married, having kids, retiring and dying. The aristocratic and wealthy classes will become true eternal oligarchs, accumulating money, power, and expertise while watching the lower classes struggle through life then die like little mayflies. Oligarch personalities would be hard to kill since they would no doubt establish safe havens where copies of their personalities could be reinstantiated. High tech worlds which give zero damns could easily fulfill this role. Imagine if Julius Caesar had personality copies in the care of trusted commanders throughout the Empire, and if the Roman Senate were the undying personality copies of the original senators filled with renewed youth and vigor every 75 years? It would change everything. Imagine if Queen Victoria or Chairman Mao had the same capability. The OTU will never be the same.
This could have been a powerful motivator for the Civil War. Olav hault Plankwell could've wanted to blow the whole pack of ancient worthies into radioactive slag just to get the Imperium out of their suffocating grip. It would be a good reason for his troops to follow him across the space Rubicon too, since the lower classes would most likely be pretty tired of it not to mention envious.
Other issues include having multiple copies of the same person operating independently. It doesn't matter is it's illegal or socially unacceptable, if it's possible it will happen. What if the Imperium faced 100 Ivan Wolfes in the Solomani Rim War instead of just the one? As if the Solomani won't clone their finest military minds in preparation for the next war? As if the Imperium won't do the same? What if the best most experienced non-coms and officers were recorded, duplicated and used to raise armies like the Clone Army in Star Wars? It is now possible in Traveller. Instant colonization of planets with copies of designer personalities in cloned bodies all happily working away for whichever power owns the project. Lonely people could have their dream spouse designed and decanted, not too expensive for someone who has multiple lifetimes of investments to buy it from an amoral megacorporation or high tech world. The Traveller Universe is not a moral place, and if these things are technologically possible they will happen.
I think this is a really bad idea, and placing handwavy restrictions on it is just a tatty band-aid which detracts from the suspension of disbelief even more. We would have to know exactly how it works to know if there are reliability problems with it, and even if there are, a tech level 15 society wouldn't just stop working on it when all the powerful people would want it.
If this is going to be a part of T5, then T5 needs to embrace nanotech, biotech, cybertech and transhumanism and adapt the reality of the OTU setting to them, or just wallow in a tar pit of excuses as to why these technologies exist but their consequences don't, a bit like how the Solomani are supposed to be masters of genetic engineering but with 1000 years of practice all they've done is NOTHING except create sentient dolphins and apes.