Haha, it appears you cannot win! Most of the hotels match the shape of the cake table to the table shapes they use for the dinner tables. Although here, I just say, the cake tables usually are round. Funny thing is here I find some of them quite small, so there is not much room to decorate the table. So this is likely a regional thing, depending on where you live.
Haha, yes, I think rectangular or square are nice too, especially with a square cake. We don't see them here often. Actually though any shape will go with any shape of cake. I think that was more the norm, years ago - using square or rectangular tables, at least here it was. In fact having the cake on the head table directly in the centre was the norm for many years.
I also like the idea of the cake being on a pedestal, those concrete or plaster type ones, with something on top as the table part. However, I guess you really have to make sure these are stable too. Plexiglass with two or more pedestals underneath (columns) makes a stable base and you can cover the plexiglass with material.
But honestly, some folks could make a cardboard box look elegant, haha!
You brought up am important part, balance. There are ways of making a too large table look more balanced with a smaller cake. Ways of adding around the base of the cake to make it appear larger, or raising it up so it looks more balanced in proportion and this is important too. Puffing up material around the bottom will make it appear that the cake is larger. Putting bowls of flowers or candles or other decorative items around the cake base help too.
I rather like having control over the cake table, mainly because I have made cakes for a few celebrations where the cake was a very elegant design, and was placed on a banquet table that was covered with a sheet of vinyl with all all of the creases showing. Now for some folks, the table set up is not important and budget and time and taste all enter into the decision, but honestly I would rather do the display and set up for free than put an elegant design in a setting like this. I suspect this is what the wedding coordinator meant when she said it should be left up to the professionals, she has likely seen some displays like this too. But some folks without any expertise or experience do an absolutely fabulous job!
I think that setting up a nice display table is like anything else. Some folks are naturals at it, some can learn and some don't really see it as important and perhaps don't take the time to do it as well as they might. We all have different talents and degrees of design abilities.
I find that a lot of folks think tulle is too old-fashioned or boring, but personally, I think you can do a lot with it, it is reasonably priced, it adapts well and doesn't wrinkle up or crease, you can attach it easily and it is readily available in a variety of colours. Organza has similar qualities too. But then, you can use almost any fabric and do a lovely job. There are some wonderful fabrics that are meant to be used for curtain linings that have a beautiful sheen and design. You can buy remnants at good prices, you can use curtain laces and fabrics and these are nice and wide as is tablecloth fabric and sheeting. Most fabrics can be bunched or turned under eliminating the need for hemming the ends to finish them. You need to see if a fabric will drape well, will hang or bunch of nicely. The weight of the fabric and type of fabric determine this. Some fabrics are just too stiff for this use but might be great for covering a cake board. And you can do a fantastic job on a dime or hundreds of dollars.
Also, if you can try to duplicate the setting at home and do a dry run, it is usually a good idea. Sometimes I mark off the diameter of the table in question, with a piece of fabric or a board cut to the size. Then I play with the set-up.