Why don't we just use combination AFCI/GFCI breakers for every circuit in a home?
Sure, go for it

There's no basic problem with what you propose.  Feel free to put CAFCIs in all breaker positions.  

You may have a problem finding AFCIs larger than 20/30 amps, and you may have trouble finding 2-pole AFCIs in some cases.  In this instance, for equivalent protection where AFCI is not mandated, simply run those circuits in metal conduit, e.g. EMT/THHN wire.  This will protect the wire, not the appliances.