Tried it lot's of times in my early planted tank effort's before I knew any better.
Have grown them in pot's in cichlid tanks where the fishes would otherwise root em up,and still grow em in my tanks now.
Have yet to grow them very well without soil based substrate and or root tabs.
Nearly all the Sword plants develop extensive root ball or mass that takes nearly two hands to hold but not likely without some type of fertilization.
They will attempt to use nutrient's they can store in their root system's at first,but then slowly deteriorate when these are used up and no other nutrient's can be easily found.(might last a month or two)
Not a plant I would hope to grow large/ healthy without consistent nutrient source.
I used to have to pull the potted swords from the tanks with cichlids about every six month's and re pot them with soil capped with sand, or aquarium gravel.
One can easily make the case that all plants need consistent nutrient source to perform well.
Fast growing plant's like the Sword plants,easily demand more than most all other's.
I have a bunch of them growing in my 20G. My substrate is just black gravel; I put root tabs under the plants every 4 months (when I remember) and they grow wonderfully. They grew fine before I used the root tabs, but the leaves were smaller and it grew slower. It's doable but I think you'll get better results if you at least give their roots something to feed on :>>
Amazon sword's not suited for tanks smaller than 60 gal .(column tanks work well) IMHO
Healthy Amazon sword 's Can grow a couple feet tall and nearly as large around in short order.Root wad big as a dinner plate.
They need room to grow up/out which isn't available in 10 to 20 gal tanks.
There are some hybrid Echinodorus species that do not grow as large as the Amazon swords.
I'm growing Echinodorus Rose,Echinodorus Red Flame,Echinodorus Kliener Bar,in 80 gal and 55 gal and they grow only slightly smaller, but all send our runner's from over the top of the tanks a couple times a month.
I am taking some plantlet's from them this weekend to trade for store credit at LFS.
For small 10,20 gal tanks I might look at plant's like Crypt Pontederiifolia that grows to around 10 inches tall to maybe a foot, and sends out runner's fairly frequently in good condition's.
Or maybe plant like Echinodorus Vesuvius to help fill space in the tank that most use the Sword plant's for.
Nobody purposely places plant's in their tanks that they want to become stunted possibly, or whither and die from lack of nutrient's.
No I think not,they want them all to perform well, and grow larger and as mentioned..a Healthy Amazon sword such as OP mention's will quickly grow up/out of the tank and possibly rob nutrient's from surrounding root area to the point that other plant's anywhere close, begin to perform poorly.
Roadmaster's answers seem complete to me. Good info and advice.
I have one sword in my 40b, purchased ~6 weeks ago at 6". My substrate is BDBS, with root tabs and other ferts. No dirt in this one.
It is now spreading leaves across the top surface, and I'm hoping to get it moved over to a new 55g setup for more height. It'll likely push at the front and back then, but at least it'll have more height. Awesome plant, looks great. It's growing well outta sand, for now. Lots of other plants, all doing well.
I have some mico/mini swords (no idea what these actually are), with leaves the same sword shape, but scaled down to a max of 5" height. Had those for two years now. In hindsight, I wish I had more of those for the 40b, instead of the monster.