"This will more than likely mean these (western) games will only be there for a year or two then disappear"
I'm not sure this is set in stone quite yet, to be honest. If Nintendo doesn't have good third party support on the Switch long term, it'll have more to do with them not having the audience. It won't be because of power. I think they can have the audience, because I think too many people are underestimating just how many people value portability over horsepower.
The Switch isn't a console/handheld hybrid - it's a console's functional equivalent to a laptop. It's a totally different beast altogether. No one who has a laptop wishes that they had a more powerful home computer instead. The only people who would rather have a home computer are enthusiasts or people who have specific jobs that require them. Most people do more than get by with a laptop, because most people don't need that power.
I think the same will be of the Switch. Most people who play games play them casually - they aren't enthusiasts like us. Let's not even talk about leaving your house for a second - there are a lot of people who will find immense value just in being able to sit in bed with the Switch plugged into a charger (like with the Gamepad). There's a real argument to be made over whether the best version of a game like GTA6 will be the most powerful one or the most flexible one, and a lot of people will go for the latter.
If you asked me if I would rather watch Youtube on my TV in 4K, or on my laptop at only 720p, I would pick my laptop every time because I am almost never home and 720p is frankly more than enough. I think that a lot more people than anyone thinks is going to find that more valuable, which means that every multi-platform game will have a real financial incentive to port their games to the Switch.
I say that the audience is what's important because if people don't associate the Switch with multi-platform games by the end of its first year, the thing is done. That comes down to associative marketing. If Nintendo wants third party games, they have to market the Switch as a third party, multiplat system first and foremost. That means marketing deals with EA and Take-Two for their sports game commercials. Every Madden 2018 commercial has to have the actors playing the game on the Switch exclusively, with their new "No Play Like It" slogan at the end of every one. If there is a big shooter or open world game coming out next year, Nintendo needs to nab exclusive marketing rights for it. Every ad for something like Mass Effect: Andromeda has to be played on the Switch, highlighting its portability as more valuable than its fidelity, with "No Play Like It" at the end. If there aren't people who mistakenly think that a the third party games are exclusive to the Switch because of the way the games were marketed, then Nintendo is doing something wrong. There were people who thought that Destiny was a Sony exclusive. Nintendo has to do that for the Switch many times over, and they have to do it by holiday of next year.
They do that for a year, and they will have excellent 3rd party support. I don't think they'll ever get to a point where it's ubiquitous because some games are just too complex, but most games frankly are not. Most games are prettier versions of last gen ideas, and Switch games don't need to be that pretty. Taking Red Dead Redemption 2 as an example, if that game was ported to the Switch but only looked like the original Red Dead Redemption on the PS360, most people wouldn't care or notice. The form factor gives it that leeway. I think that they can definitely get to a point where 85% of third party games that are made are put on the system, and thats a more than good enough number.
If they do that (on top of some other OS/Account-based stuff), I have every confidence saying that the Switch will be the second Wii- no, the second Nintendo DS phenomenon for them. It will, quite literally, take over the world. This idea is that good. Especially when you factor in how much mindshare they are setting themselves up for next year. They'll have the Switch out, a steady stream of exclusive games all year round pretty much guaranteed, Super Mario Run will have come out, they'll likely have the two mobile games coming out on top of newly announced ones, they're probable going to announce their first film next year with possibly a trailer, and you're probably going to hear more about their theme park in concrete details. Nintendo is going to have a lot of momentum next year from things that have nothing to do with their video games, and that has everything to do with their video games because it's going to make their brand positive again.