it can suspend all kinds of services on your console, up to and including bricking it completely.

No, just online services.

Xbox and PlayStation have the same terms & conditions. Why is Nintendo being singled out?

Xbox:

You will not attempt to defeat or circumvent any Xbox Console, Kinect Sensor or Authorised Accessory technical limitation, security or anti-piracy system. If You do, Your Xbox Console, Kinect Sensor or Authorised Accessory may stop working permanently at that time or after a later Xbox Software update.

PlayStation:

we reserve the right to take any action we believe necessary to remedy the violation or to protect SIE’s interests, including: (a) the automatic removal or blockage of content associated with those Accounts; (b) implementation of upgrades or devices intended to discontinue unauthorized use; (c) the permanent or temporary disablement of access to any PSN Content, PlayStation Devices, products, services or features; (d) notifying law enforcement or the appropriate authority; and (e) initiating legal action.

edit: added some more words from the respective ToS to make it more legible