Is there a mobile phone available in the market with printing facility?

To start with, if you want to take a print out directly from your phone, you don't need to get a special phone for that. if you are having a smartphone in recent days, this option would be available from all of them.
Here's how:
The best method to print from an Android smartphone, from an iPhone or iPad is to establish a connection between your device and your home or office network. Nowadays almost every Android smartphone and tablet that runs on a 4.4 or higher version would come with a built-in wireless printing functionality.
All you need to for it would be downloading a relevant app that is compatible with the printer you are going to use.
Currently, most of the printer manufacturers launch their free apps on the Google Play Store that would automatically enable the users to transfer the print jobs to a selected printer.

With Google Cloud Print now a regular feature in Android smartphones running the latest versions like Nougat, almost all the latest phones have this facility. You are right when you say new mobile phones are being released with tons of features. Printing mechanism is something that is and was always a part of the Operating System which talked to a compatible wired or wireless printer on the network through software or firmware drivers that were provided usually by the printer manufacturer. In newer Androids you now have printing as an inbuilt facility using the Google Cloud Print option which you can easily discover in the settings using the search feature or 'Printing' section in the 'System' settings.

You can easily exploit this feature to print wirelessly to a printer on the same network or even through a USB port using a OTG cable.

Alternatively, many printer makers offer some or the other kind of on-the-go e-print application that you can download from the Play Store or the manufacturers website and install on your mobile. This shouldn't be too much to ask for as that's the way smartphones work – Through apps. Almost all the inbuilt mechanisms you see in the smartphone have an app that controls them – which of course could be a system app or an installed one.

If you are an iPad or iPhone user your phone can get the better of you, look for an AirPrint printer in your near vicinity and start printing – but luckily not many of them going around.