Does every rack-mounted device need rear support as well as front mounting ears?

No. Plenty of lightweight, shallow rack equipment is designed to hang perfectly happily from its front mounting ears.

Heavier or deeper equipment is a different matter. Some devices require rear support brackets, fixed rails or sliding rails, and the manufacturer's mounting instructions should take precedence.

A shallow patch panel and a deep UPS may both be described as “rack mounted”, but mechanically they’re asking rather different things of the cabinet. Don’t assume the front ears are sufficient simply because the device can initially be persuaded to hang from them.

Where additional support is specified, use it.