I'm not saying it's impossible, but it comes back to the fact you'd be adding yet more and likely lower performance targets for games to hit, where the Series S is already struggling, plus potentially breaking compatibility for games that just can't run when portable. That's a rather messy proposition.

Plus, $500 is too steep for a handheld, at that price it will only sell to a niche audience of enthusiasts like Steam Deck.

What Microsoft doesn't get credit for these days is it's flexible software stack that does a lot of the hard work in abstracting different hardware environments which allows for a degree of flexibility in the hardware it can run with, without requiring much work on game developers behalf.

In short, Microsoft doesn't actually need identical hardware to the Xbox Series S to achieve compatibility, it has already established the software hooks/switches, so that if you load a Series X game, the device can tell it to run it in a "Series S mode".

Thus you only need to exceed the Series S hardware capabilities.

It's similar to backwards compatibility on the Series S, it has the hooks established so if you run an OG Xbox, Xbox 360 or Xbox One game, it will tell the games it's an Xbox One S and run those titles in that mode.

Remember the Xbox Series S is just an old 8-core Zen 2 complex, 10GB of Ram and a Radeon 6500XT class GPU... It's pretty low-end.

It seems pretty clear to me that Microsoft's long-term strategy is to get completely out of the gaming hardware business. So, I can't see them trying to get into a new segment of that business.

Even if it sells as few as 5 million units, I'd consider that successful enough to more than warrants its existence. The cool thing about these "SteamDeck style" handhelds is that they don't need to sell much in order to get supported. A Series S handheld would be a much better system than the Vita even if it sells a fraction of what the Vita sold. And since it's not competing over resources with its home console counterpart, there is no serious downside to it as long as it's not mandated for more demanding games.

An additional userbase of 5 million may translate to a 7-10% increase in software sales and subscriptions.

I can't see Microsoft going to all the effort of a handheld Xbox Series just for another 5 million sales.

I don't think that would lead to 10% more software sales or subscriptions either as there would be overlap of some people who already own a Series S/X getting one to play their existing library and subscription on, plus some of the buyers would be people who would've otherwise just gotten an X or an S anyway so it's a sale they would already have gotten instead of an addition.

Yes I had all of this in mind but perhaps an increase of 5-8% is a more realistic range. But if Microsoft price it low and sell it at a moderate loss, 5 million units could be passed with relative ease. I think it has the potential to bring in a few million new gamers who wouldn't get into the Xbox ecosystem otherwise.

I disagree, MS isn't looking to get out of creating their own hardware instead they are looking to get out of depending on hardware sells as the sole means of revenue in games.  In other words, MS doesn't want to depend on the sales of Xbox hardware for revenue when there are billion of other devices out their that can play games.  Why limit your market just to a console when you can at least attempt to allow users to play on whatever they have on hand.  It also leverages the strength of MS as a company including their cloud stack.

I get what you say and kind of good advice in general but it's a little more complicated than this. Tflops measure the limits in compute power a chip can have at corresponding clocks. It is actually very precise to determine the capacity of a chip in a nutshell. However, this is only 1 part of the story the others can all be summed up by what % you can actually use in any given scenario or in other words, how starved the chip actually is. It can be starved with an insufficient memory pool, insufficient memory bandwidth, and insufficient power delivery. 

Another aspect to consider is the amount and variety of hardware acceleration you have that may result in software bypassing the utilization of CU in some scenarios where it would need to use them on a chip without such acceleration.

in the example you gave the 2700U is actually very starved by the lack of memory pool and bandwidth, The 4500U feature 50% more L2 cache and 2x L3 cache and supports higher memory frequency. The Cpu side is also more power-hungry with the 2700U than the 4500u leaving more leeway for the GPU on the 4500u to use the same 25W TDP.

However were you to use the vega10 featured in the 2700u@1300mhz and the vega6 of the 4500u@1500mhz in a context where there are no bottlenecks the Vega 10 would result in better performance than the vega6 as their respective max capacity would be the actual bottleneck. 

For the 5500u vs 4700u, the sole difference is that the Cpu side is less power hungry with the 5500U allowing for higher clocks on the GPU, but make no mistake if you were to isolate the GPU power consumption and compare them both the 4700U would actually be more efficient per watt. Even the more recent rdna2 is most efficient at around 1300 to 1400 MHZ according to this source. The Vega architecture however had a much lower most efficiency clock speed, I could not find a source for this but I remember at the time of the Vega announcement that AMD was using clocks of ~850MHZ in their presentation to portray efficiency increase compared with the older architecture. This was prior to the reveal of the Vega 56 and 64 however so it is possible that it was tested on engineering samples. This may have shifted with node shrinkage also, but could not find anything on this, still really doubt 1800mhz would be more efficient per watt than 1500mhz with the Vega architecture.

All that said, however, MS having access to semi-custom architecture and being designed for a gaming-first application they would make sure the GPU power (Tflops) is actually the bottleneck in the vast majority of scenarios so as not to create unnecessary starvation of the GPU. In such a scenario, where GPU power (Tflops) is the bottleneck and on the same architecture, then it is relevant and accurate to a relatively high degree, to use such value as a point of comparison. if they were to switch to rdna3 or rdna4 instead of just shrinking the fab nods of their semi-custom rdna2 then it would just be icing on the cake as it will feature more hardware acceleration possibilities.

Yes 500$ is a little high, 400$ would be more reasonable, but compared to the ayaneo2 at $1000+ and with even more performance I would still go for it at 500$.

That said I think MS would have a little more leeway to cater a tad more to enthusiasts than pure mass market with such device. As it not being critical to their overall strategy.

The main reason I am a little skeptical of it actually happening is that it's a big commitment to make a whole portable/hybrid Xbox Series just to sell a few million units. With how Microsoft has been emphasizing Xbox hardware less and less in recent years, I'm just not sure I see them pushing for something so ambitious.