Illegal is probably too strong a word as it normally implies a criminal act.

Cycling on footpaths and on private/access land may be trespass, which is generally a civil law matter solely between the trespasser and the landowner (unless bylaws in place). It is not generally a criminal law matter.

A lot of these concerns are easily managed already:

Go to Strava settings on PC/MAC:
Go to Privacy Settings:

Consider using these:

Privacy Mode: Enhanced
Create Privacy Zones (a no brainer for security)
Flyby – Nobody
Group Activity Enhanced Privacy: Check
Strava Metro & Heatmap: Uncheck, so data not included

Other Options:
Hide from Public Leaderboards (can also do on ride by ride basis)
All Private (can also do on ride by ride basis)