its to weak to run them without heavy rework. In terms of performance, especially in handheld mode, its basically a PS3/Xbox 360 and not a PS4/Xbox One. One of the reasons many people wished nintendo would have used the new Tegra X2 chip instead the 2year old outdated X1.
Your general sentiment is correct. The Tegra X1 is slightly more modern than the PS4 and Xbox One's GPU, which means that in terms of features these GPUs are much closer to each other than say the Switch is to PS3/Xbox 360. On the other hand in terms of raw computational performance Switch is closer to Xbox 360 and PS3 (about on par with those two in handheld mode, and about 1.8X-2X faster in docked mode). This means that most modern engines will support Switch, but ultimately the games that can be ported on it will depend on whether they are computationally intensive (many Western AAA titles are, so those will most likely not run well and not really be practical to port) or not (there are still quite a large number of games, particularly from Japan that are not).
Also, the X2 is not really that much better than the X1. The biggest improvement on the X2 is memory bandwidth, which has been doubled. In addition, X2 achieves a maximum of 750 GFLOPS in single precision mode (the X1 could do a maximum of 512). Now Nintendo, most likely in a bid to keep up with the system's thermals, down clocked the GPU so the Switch's actual performance in docked mode is about 1.3X less (about 393 GFLOPS). If we reduce the speed of the X2's GPU by the same amount, then we get about 576 GLOPS. While that should provide some boost to certain games, it would still not be nearly large enough for computationally intensive games that struggle to run on the base Xbox One and/or PS4 to come over. In addition, the X2's GPU microarchitecture is based on Pascal which is more of a refinement to the Maxwell based GPU found on the X1. The jump from an X1 to an X2 is just slightly more than the jump from the 3DS to New 3DS, but it would not make more on-par with PS4 and Xbox One with regards to computational performance.
The reality is that the Switch's emphasis on portability meant that they had to with hardware found in mobile tablets (these run at around 4-10 watts), and there are very few options available at the time the Switch was being internally developed or even now that would allow for the creation of a $300 handheld that would be on-par with PS4 and Xbox One.
Because the AAA games (Witcher 3, Shadow of Mordor, Tomb Raider, Monster Hunter World) you want barely run in 30fps on a PS4. So porting those to the Switch takes lots of effort. More than a simple resolution drop for sure.
I totally agree with Witcher 3 and I would lean towards agreeing with you MHW (though I am still uncertain about that; because the game is clearly large and so Switch might not be able to run it, but on the other hand it is running on a last-gen engine though of course the engine is not everything when it comes to making a game run on a certain platform). But Shadow of Mordor and Tomb Raider (both the 2013 game and Rise of the Tomb Raider) run on Xbox 360 and/or PS3, so these should be more than doable on Switch. In fact, Tomb Raider 2013 was ported by Nvidia (on-behalf of Square Enix) to the Nvidia Shield and based on my experience with it, it runs quite well.