The common thread among your first three examples is that they are verbs. Things that are able to 'do' those verbs may then be suffixed with -able.
This is the same with other words like write (writeable), read (readable), eat (eatable / edible), etc.
Obsolete is not normally considered to be a verb (it's an adjective), so is modified differently (e.g. obsolescence).
The following dictionary entry mentions that obsolete may be used as a verb:
[with object] chiefly US
Cause (a product or idea) to become obsolete by replacing it with something new: we’re trying to stimulate the business by obsoleting last year’s designs
The form obsoletable may be used in that sense. Here's an example:
Coloring the cards only works for nonperishable and non-obsoletable items.
- Manufacturing Consulting Services, Inc
As @PLL notes, obsolesce is the proper verb form of obsolete. Here's the dictionary entry
Obsolesce derived verb
(derived from obsolescent: Becoming obsolete)
existing systems begin to obsolesce