Depends where you are. Many places as a designer you physically can not touch the board due to union rules. Also, yes, it is the designers job to look at the whole picture and not at the console. Programmers know their consoles in and out, left and right, backwards and forwards. Its their job to know exacly what every moving light on the rig can do, its their job to know what all the console can do. A good programmer can make or break a show, especially when you get into moving lights of any kind.
Point blank reasoning ahead:
The reason you can program a show faster then spouting numbers is because you do not know what you want. Being able to just adjust a sub or a
channel quickly without thinking about it and telling it to someone else does make things faster, but at the same time you are doing a dis-service to yourself. When you walk into a space, its your job to make sure that you have all the paperwork you need and its correct, your job is to get that into the console with the aid of the programmer. You should walk in with detailed cue sheets that give rough levels. Get those into the console then go adjust, don't try to create stuff on the fly.
Now... the board op vs. the programmer debate. A board op is someone that gets paid to sit their and press go. They should know enough about the console to do typical show run things and maybe some troubleshooting. A programmer is someone that usually has a degree and is highly specialized on one or more console. They should know thier console in and out and everything they possible could know about it. They should also have extensive moving light knowledge. They are there to assist the designer in getting their vision onstage in a quick and orderly manor. Usually a programmer comes in for tech and leaves when the show opens (for longer running shows), a board op comes in and pushes go.
Basically, get used to it if you want to be a real designer. You can't
go up on a ladder and focus your own lights, why program the console. Being a designer means the only button you should ever push is the button on your com to change a level.
oh... and HUGE pet peave... don't speak "board" to the programmer.... just say in plain English 75 at 25, update... none of this 75 at 25, update cue 25, or even worse.. the 00 thing... even though I sometimes do that...