It is all about efficiency, stability, and control.
First stability and control:
In both a canard and a traditional layout, the main lifting surface is the wing, and the canard or the horizontal tail provides the stability in the pitch axis. In a properly designed stable configuration, increasing pitch gets you to higher angle of attack and eventually the wing stalls, but the horizontal tail still provides effective pitch control. If the wing is designed properly, the ailerons will still (and are now required to by the FARs) provide roll control through the stall. The FARs don't say that exactly, but the pilot is not supposed to have to provide extraordinary effort to control the airplane through stall. The Glasair Glastar and Sportsman are designed this way. You can keep the stick back through the stall you will feel the break, keep the stick back and it will be buffeting, but you can use the ailerons to continue to provide roll control. Just relieve the back pressure a little and the buffeting goes away and off you go.
It is an interesting and cool ride.
As as stable canard configuration approaches higher angle of attack, in order for it to be stable, the canard must stall first so the airplane will pitch down to recover from a stall. Interpretation: your pitch control will be non-effective through that maneuver
You do however maintain roll control through stall because the main wing doesn't stall, and that is where your roll control is.
A normal airplane configuration is designed to have the wing get to 100% of its capability at stall, or rather its lifting capacity is defined by the stall. You can also put flaps, slats, etc... on the wing to really make it lift like crazy. Really you can do all that you can, as long as it is stable and you can control it.
In a stable canard configuration, the wing never gets to its maximum lifting capability because the canard must stall first and the airplane pitches down. Adding flaps provides additional issues. (Starship
Three surface airplanes:
The Peterson machine is quite impressive, but is not technically a canard configuration. It is a three surface airplane, as is the Piaggio Avanti. There are specific reasons to use this configuration and from what is published, the Katmai is quite effective at allowing slow flight, stabilty, and control.
The real question might be, why don't we all have 3 surface airplanes