It's not just about reducing error (although it does that really well too.) It's also about increasing transparency, for two reasons: it makes many things explicit that would otherwise be easy to hide, perhaps by accident; it also provides very strong support for querying your finances in various ways.
Whenever I'm budgeting for something (a project among friends, the wedding with my wife, and so on) I always try to start out "simpler" but I also always end up doing something like double-entry bookkeeping because all other "simpler" solutions make it very hard to figure out where money is actually coming from and where it is going.
This is as good a place as any to start: https://plaintextaccounting.org/