As others mentioned, the button compass was originally a WWII evasion aid, meant to be used with the silk "escape maps" which were a very large scale, not much terrain detail. The compass was only useful to tell general direction and that because most travel would be best done at night or during limited visibility. I have a few of the tritium (long dead) military button compasses, some have a light lanyard and others have none. The compass was originally designed with swallowing in mind. If a person was captured they could retrieve the compass later....yeah, don't ask.
I personally don't carry one for outdoor trips. I can usually find direction as accurately as a button compass providing there are no clouds blocking navigation aids in the sky. I do carry 2 compasses, a Silva Ranger and a Silva Huntsman in my PSK.
I might add that today's Evasion charts are smaller scale, 1:250K or 1:500K and printed on Tyvek paper. Some have local survival information printed on them and are quite bulky to carry but durable and waterproof.
Cheers!

I carry a NATO Survival
Brass Button Compass made by Pyser-SGI. Accurate, tiny and very well made but pricey at almost $30. (U.S.). I carry it in a small aluminum medicine "tube" on my keychain along with my ARC AAA-P light, fox whistle, Sliver gripper and a few bronze safety pins (u.s. issue).