I doubt I could even find a company that prohibited accessing LinkedIn from a work computer anymore. Many don't disallow installing software either.
If you truly believe what you wrote, you almost certainly believe accessing work email from a personal device is prohibited at typical companies. Maybe this is true at large companies, but not anywhere I've worked.
Your argument has no validity. You claim that it's absurd for IT to differentiate between "sending your email to your phone" and "sending your email through a third party with no connection to email deliverability and no business relationship"
Countless companies prohibit salespeople from connecting to potential leads on linkedin to prevent it leaking to competitors.
I'm guessing you've not worked in enterprise because it's pretty normal to have a company policy on "bring-your-own-device" (typically companies will only allow access from devices that meet security requirements on password, anti-virus, etc. often they'll also require the ability to remotely wipe your device)