Sony is missing a lot from this while they are trying to compete with Apple and Samsung which they cannot win. 
They are missing a lot with this one where ASUS and Razer phone is getting a traction. This should have done by Sony and they are getting to catch up game again syndrome again. Mobile gaming is getting bigger and bigger. 

I know I know they already tried this before but they really didn't tried that hard.

Take a look at the twin view docks. They could create an add on dock that will enable your Xperia phone to be able to play your  Playstation 4 games on the go. I mean phone are essential in a daily lives of a person now. They can gather a niche then they can expand on it. All the power will be done thru the accessory and the phone will be your display that will also help with processing the power thru the games.

Maybe they are thinking of doing it because they saw the potential with how successful the Switch is.

Well, the problem is that you would need to bring the accessories with you, not just the phone - and these seem to be rather bulky to me. The Xperia Play at least was ready for playing out of the box.

But I agree that they could release a new Xperia Play with similar hardware than the ROG, just like the Play with built-in controls. Add a big battery and I wouldn't mind if my phone would be big and heavy, at least it would do so with a purpose.

While we're on it, I expect Nintendo to bring a Switch Phone around 2020 (without removable Joycons but otherwise similar in design to the Switch)

Yes.

Sony needs to stop playing being a Google charity, and start selling a PlayStation Phone. Since they bought complete control of their Mobile division, they have lost $5 Billion. In that same time they have made $5 Billion with PlayStation. So basically they have not made a single dollar from PS4, because all of the profits it's made, were eaten by Sony Mobile.

Sony needs to drop Xperia and Android, and release a PlayStation Phone. A Ryzen and Navi Mobile based Phone, that shares the same OS and Library as PS5, with full PS4 B/C is what they need. They don't have to set the world on fire. They can sell a few million a year, and they will be in a much better position than they are right now. It is not about mass market, they are never going to win that. They need to focus on making a device like PS4 that cover a small but profitable sector of the population.

With a PlayStation Phone that has a shared Acrchitecture, OS, and Library with PS5, Sony will share R&D across both devices. Every unit sold will either add a user to their ecosystem, or increase the time and money spent by current users. This would be far superior to having a Home and Handheld with seperate Architectures, OS, and Library as they have had in the past. It would be worlds better than having a Home Console, a Handheld, and a Phone all running completely different paths, especially with one directly competing with the others, while draining all profits made by the bread winning products.

Sony would be in a much better position with a userbase of even 10 million PS Phone users than they will ever be with 100's of millions of Android users. At the end of the day, Sony has no relationship with Android users beyond Point of Sale. After Sony sells and looses money on Android, Google starts picking up 30% of every dollar a user generates on the platform. With a PS Phone running on their own OS and powered by PS Store, they would pick up that 30%, and they would continue to have a relationship with their consumer as long as they use the device.

If they went this route, I have no doubt, even if it is limited compaired to Android and iOS as far as apps go, that it would be successful. If PS Phone offers all 1st party Sony titles going forward on day one, and all major PlayStation 3rd party titles day one, in a shared library with the home console, ala PS4 and PS4 Pro, then they will easily find a Profitable and Sustainable userbase.

Right now Sony is continueing to loose 100's of million a year on Xperia, while it competes directly against their ecosystem, and adds to a competitors bottom line. All while their most valuable assets (PlayStation Software, PlayStation Network, and PlayStation Store) are not available on a Mobile device. This needs to change if they ever want to stop loosing money on mobile, and continue growing and strengthening their own ecosystem.

I would say they need a hybrid PS OS + Android OS.  Users wont buy if they cant have the apps they use on the device.

I'm a huge Xperia fan, and I always buy Sony smartphones. I love the remote play feature, and an Playstation Phone (like they did with the Xperia Play and the Xperia S) with exclusive games, like a new Vita, would be a moderate success.

Few problems with that.

1. Android and Android Apps are built around ARM, PlayStation and PlayStation Software are built around X86.

2. Sony has proven they can't handle 2 OS's successfully with teams focused d on each. Having one platform with two OS's would be even more of a struggle.

3. It still has them selling a competitors product.

For these reasons I think Sony should just double down on 1 PlayStation Phone, that shares all assets with PS5. Give 100% focus to this Phone, and focus exclusively on the most core gamers who care about Games over apps. As long as they have a good Internet Browser, they can achieve everyhing Apps offer, and at a high quality most of the time.

Again, they don't need to focus on reaching 20, 50, 100, or 200 Million sales. They need to focus on making a Phone that is profitable and completely geared towards a specific audience. That is what they excel at. PlayStation 4 is just a closed garden PC that mainly focuses on Games and Entertainment. It is less than 1/10th the PC market in yearly sales, but it is earns them billions in profits each year. 

I don't think Sony need to get into this specific market. 

1. Yes they are they are competing within the circles of Apple and Samsung at the same time sandwiched with less popular phone. If they want their phones to explode then they need to do something different. No Company will just being happy with being profitable or only profiting little. 

2. What I meant is not just the specs but a phone dedicated for games that will have their own portfolio of games, exclusive add on an such like ROG Phone is having.

3. It will be bigger as time goes not just with gatcha games but with solid games.

4. you don't need internet. 

5. because that can potentially sell their phones. They might find success again in trying again to have their phone lines have exclusive game feature that is not available on other phones.

Yes it is. But they need to divide their resource to make another gadget.

For now SCIE are full with PS4 , PS VR, PS Now, PS Online, Games Studios and future PS5 . Just let they focusing on PS5 first and let PS brand getting more bigger. Once the time comes, i think they will making it in the end.

SCIE doesn’t need to fully support it. Sony already has Forwardwork that is dedicated for mobile.

It’s their phone division that needs to do it. Build up a studio for it. Like Sony Music they are the ones handling Fate on mobile. 

Or outsourcing from 3rd party devs.