[DatePicker] Support focused input in open state

[amok]

I'd like to keep input focused/active when desktop calendar is open.

• I have searched the issues of this repository and believe that this is not a duplicate.

Summary 💡

MUI-pickers version: 4.0.0-alpha.9 (see deps below)

I looked through the code, issues, API docs and did not find any proper solution.
As far as I understand DesktopWrapper has "hardcoded" role="dialog"

https://github.com/mui-org/material-ui-pickers/blob/6ffb24b2ff995658f06bebe4fda4759276e83d96/lib/src/wrappers/DesktopWrapper.tsx#L37

which makes TrapFocus of PickerPopper to enforce focused state on a Calendar element

https://github.com/mui-org/material-ui-pickers/blob/6ffb24b2ff995658f06bebe4fda4759276e83d96/lib/src/_shared/PickersPopper.tsx#L120

Examples 🌈

https://monosnap.com/file/CtU6UsH6Rl49MdJXEFrar06fxHuUbY

Motivation 🔦

I'm trying to achieve the following behaviour:
When input is clicked - open calendar but keep the input focused and active.
DateRangePicker already supports this behaviour, see attached video and check https://next.material-ui-pickers.dev/demo/daterangepicker#basic-usage

    "@material-ui/core": "^4.9.13",
    "@material-ui/icons": "^4.9.1",
    "@material-ui/lab": "^4.0.0-alpha.56",
    "@material-ui/pickers": "^4.0.0-alpha.9",

[lamhungypl]

#1817 #1998.I am also waiting for this behavior.

[Serzh470]

I support this too, this behavior will be aligned with material design templates:
Desktop pickers