It is hard to say how crucial it is to put games on the table as a designer. The only reason that it is so hard is the fact that there might not be anything more important, so I'm thinking 10 or 11 on a scale of 1 to 10. Probably 11.
Since I started designing games, I've been putting games on the table on a regular basis. Small games, medium games, big games, cards, boards and anything you can think of. The secret is not letting yourself stop designing, because like many things in life, the best way to improve is to learn from experience. Yes, please do fail as much as you can. There are board games that I put aside after 1 play test and they are there ever since, and those might be the ones I learned the most from.
Always have gaming supplies at the ready. Don't delay a prototype because you are out of cardstock to print on or low on printer ink. Buy a pile of wooden tokens that can support a few games (I got 2 FFG assorted sets in 6 colors on sale). Have some black dice and a permanent marker. Ever seen a professional artist’s workshop? Did you see how much stuff there is in there? Do you think they use every single thing all the time? No! Everything is there because you need to have that specific piece when Muse strikes.
Make those games! Bring it on!
In the picture you can find blank dice, just waiting for you to create your game. Go ahead you little designer, you!