Is there a way to access the phone filesystem from computer, wireless?
According to the mentioned requirements, more powerful tool to use is Sambadroid. SambaDroid is a native port for Android of the popular Samba for Linux. This application allows you to share/manage files on your device easily from any device of your network.
Update: With the Windows Creators Update you may (or not) need to first enable SMB Server/Client functionality.
Pros

No need to use router even a mobile hotpot works fine
You can easily set a share from your android device (e.g sd card)
Ability to set shared folder with read/write permissions

Limitations

Due to limitations in later editions of Windows trying to explicitly map the network drive can result in a &quot;network not found&quot; error. Ignore it and use Windows explorer method.

Requires root (needed for CIFS implementation on android). Alternatively if not root, then its better to create a shared folder on windows then access it from android with a suitable file explorer, you can still perform file operations.


Setup involves setting the desired share from the device. See screenshot:

Note: NO affiliation with the above aplication
Switch on your mobile hotspot and allow your PC to connect to the network.
Once done just type [Win]+[R] in your computer, write \\SAMBADROID
or go to PC &gt;&gt; Network and you will see a new share, see below:


The samba share will look like this:


You can perform various functions like delete, copy etc. See below:

Hope this helps.