As a counterpoint, research should be shared amongst planets, but maybe there should either be some lag as you travel further form the homeworld (measured by jump chain) particularly if a project is picked up by a different world. Sure research data can be sent around instantaneously, but the research facilities, staff availability, training, education, even the culture of a world would have an impact on it's ability to pick up and continue research done elsewhere.
Perhaps research specialization should take time to get into gear. A Power and propulsion researcher with a 25% bonus working on a P&P project on a world that hasn't done P&P research before should only get the 25% bonus at start, over time this bonus increases until finally getting the full x4 effect.
At the start when you just have a homeworld and haven't researched anywhere this specialization should be fairly fast, maybe only taking a year or something to get the full bonus. But later if you move labs elsewhere and decide for instance to make mars your power and propulsion research world it will take longer to get full specialization bonus. The length of time needed should be the one year base time, then increased by distance from home world, and perhaps also increased as your total P&P tech level increases.