Why deleting does not affect alpha channel

What you call »basic channels« are called Composite Channels and the behaviour of the Tool seems to be as intended. 

If you need to work on more than four channels simultaneously you can do that with multichannel images. 

https://community.adobe.com/t5/photoshop-ecosystem-discussions/clone-stamp-on-multiple-layers-images-at-once/m-p/3672619

Edit: That thread actually does not apply here, it was about Layers rather than Alpha Channels. 

@Kamil35425649ld03 

Such operations only work on the primary image channels of the current colour mode... So you need to "trick" Photoshop into using the alpha as a component channel. The following is untested, so I am unsure if it will work as you require.

With your RGB + Alpha channel file, use Image > Mode > Multichannel (to "split" the channels)

Then Image > Mode > CMYK (NOT convert to profile)

After using the healing tool in CMYK, return to Image > Mode > Multichannel (to "split" the channels)

Then Image > Mode > RGB (NOT convert to profile) to return to the RGB + edited Alpha channel

Hi, have you tried holding down the Shift key and selecting all the channels?