You don't seem to be playing xenophiles correctly, and I don't get why you assume that you should have vassals as a xenophile empire. I don't really understand what you mean by "integration" either
- Xenophiles have big diplomatic boosts. It's definitely easier to form federation with them. It's what I've seen in all my games when I played xenophiles. Forming federations means that you don't have to care too much about war.
- But when making wars, do liberation wars, then diplo-vassalize what you just liberated. You can even "feed" that vassal in the upcoming wars so you don't need to take care yourself of unhappy pops.
- Xenophiles usually uplift and enlighten. Which means protectorates and vassals. Protectorates are people you protect. Vassals are destined to be integrated in your empire.
- Xenophiles will have easier time to sign migration treaties.
=> the two points above means that your pop will grow faster, and be more diverse. You'll have species from your former vassals, from your allies and even from your former enemies, or even just from that neutral empire from the other side of the galaxy.
This means that you can colonize everything quickly and easily. It also means that you can outproduce other empires. Generally you won't be too good with science, but people overvalue science in Stellaris anyway - science is just a way to compensate your lack of planets and production. As a xenophile, you're not supposed to have science booms. You'll keep a normal scientific pace, allowing your protectorates to reach your level after some years (you should form protectorates early in the game anyway - if you're rarely able to transform them into vassals you're doing it wrong, you should start their enlightenment way earlier). You'll have a strong fleet that won't have a big impact on your economy.
You don't need to change the ethics of most of your pops (there can be some former "fanatic purifier" protectorate that might be a problem, but in that case it can be better to not integrate them at all).
I usually go for xenophiles/militarists/spiritualists or any combination of those three. That's a really strong combo if properly used, either in solo or even in multiplayer (especially if there are some AIs on the map). Basically, you just need to let your pop to do whatever they want, and just relocate them on the planets they arrive in. This means less micromanagement than the players who purge and relocate between planets. A spiritualist ethic convergence boost can be handy. You can focus on ship production and diplomacy, and usually you'll have a lot of influence, meaning that you can colonize a lot and suppress the few factions that don't like you until they are converted to your ways (because they eventually will). Correctly player xenophile empires should be the bigger ones on the map, with the biggest fleets and they should be late in science.
I believe that many people try to play as little xenophile empires with ethically homogeneous pops, which is not what they should do. They should make an early colonization rush. I guess they would like protectorates to be useful, but no : it's your federation friends that you should use as shields, and you should have a gib fleet on your own anyway.
It's in fact very similar to a xenophobe purger empire playstyle, except that you can grow even faster and be in a federation. Xenophiles are the best blobbers.