I am not completely sure what you mean by using three racks, but I'm picturing something like your innovative door-turned shelf at your three specified heights all on your deck.
If my mind's picture is what you are suggesting, I do not think there is much danger in setting up a vertical garden in this way, but I think you will be constrained by space and need many containers. I do not like using containers unless they have a system in place to allow for proper drainage as I don't want to play around trying to figure out how to get it right. If they do not drain well then you run into moisture related problems: root rot, downy mildew etc.
It looks like your longer planters are solidly in place, but I think that the more racks and different heights of racks you have the more mess you may be inviting, particularly if you live in a windy area or are occasionally clumsy. From my own experience as a homeowner who does her own deck maintenance of cleaning and oiling, I wouldn't want to have my garden center on my deck. The watering and weight from many racks on it doesn't seem like a good long-term plan for the deck. But, it may be that the deck is where you want your garden center because it is the most level and secure for mobility, in which case deck care is not a priority.
I personally would be more inclined to build 1) a knee height bed along the side of your house with a system for growing vertically and 2) waist-height raised beds out in the yard. In this way you are vertically gardening from a more traditional bed and you have much more space and traditional draining.
The garden bed on the side of the house idea would depend on how much sun the side of your house receives and how the bed would meet the exterior of your house (siding vs foundation etc). You could make it simply with wooden sides or with landscaping retaining wall bricks or edgers. Then I would add the vertical system for the plant to grow up from the knee high bed. I find I am more creative when I have a host of ideas to draw from. Here is a site with fifty pictures of terraced gardens or retaining walls which may give you new ideas.
I highly recommend you watch Roots and Refuge Farms' Complete Guide to Vertical Gardening. You could make waist high beds in your yard with paths between them, similar to how her garden is arranged. I'm not sure just how much vegetable gardening you want to do so I don't want to overwhelm you with the number and scope of ideas I have suggested. I recommend starting with a set-up that you know you can manage and then expanding each year.
Here are two more videos about methods for growing plants vertically using string. I find Charles Dowding to be a great resource for learn to "grow veg." I tried out vertical gardening with my tomatoes and peppers this year and followed this man's explanation of the Florida weave between two T posts, except after my tomato plants were quite large. It went well and I think would have been perfect if I would have added another post between my many plants to better secure them and started the weave at the beginning of the season.
Gardening is a wonderfully life-giving experience and I hope one of the ideas above helps answer your question so you can both enjoy growing vegetables for years to come.