Onegaishimasu. Training once a week will keep you busy enough in the beginning. It becomes "once a week, no matter what". Next thing you know, you have a practice that keeps building and growing itself, all based on that simple foundation of: "once a week, no matter what."
This sounds great but, in my opinion is just another for of "it's all ok, it's all good". No one is going to become any good this way. Period. Except maybe the person who is training once a week but doing three different arts... like many of the koryu folks did when they lived in Japan. They trained every day, just not in the same art necessarily.
You and I are part of the same organization... you know what our requirements are... The time in grade requirements for qualifying for being eligible for taking the next test are based on three to four times a week. Someone training once a week would take over ten years to do a Shodan. Since Shodan represents the point at which you can really start to train, in other words, a serious beginner, you are talking about taking over ten years just to get to the point at which it is worth the time of a teacher like Saotome Sensei to speak to you.
I just don't see any point at all in dabbling. If it's not important enough for you to make a larger commitment, then quit and find something that is. When you don't make an effort, you are far more likely to get hurt, you take up a lot of time and effort on the part of the seniors helping you with the same things over and over because you never train enough to master anything. Sure it's great to have folks who help pay the bills, but since none of us got into this because of the money (that would have been a grave error), I'd rather have a serious student who is unemployed and on a scholarship program than someone dinking around but paying dues. Now if someone really wants to support the dojo, and I have several people like this, then they can pay dues and not train. These folks can be a real help in paying the bills and I REALLY appreciate the fact that, even though they cannot train right now, they want the dojo to be there when they come back, so they pay dues each month.
But someone who doesn't think the practice is important enough to give it absolute minimum twice a week... why would they bother and why would I? As I said, anyone testing for 3rd kyu and up, can't test at my dojo unless he or she is training at least three times a week. Period.