Hi Oceanblue. Thanks for adding to the discussion! Nice to hear that a heavily planted tank with elodea (a.k.a anacharis) does do rather well as you say.
What I can derive from your post is that
The bottom is muddy, I don't clean out any debris apart from obvious rotting uneaten food!
This means you have a fertile substrate (e.g. soils) and not just gravel or sand. Therefore ferts are not as necessary as you said in this situation because the substrate provides the humic substances and mineral content. I was assuming he had an unfertile substrate like sand as most axie tanks do.
The only cleaning I do is to scrape the glass so I can sometimes see the axolotls.
It seems like you have quite a bit of algae growth on the tanks!
My point of saying that CO2 might be needed is this: plants need light AND carbon (in the form of CO2) to build more plant material. So when they have enough light and not enough carbon, they cannot even use some of that light! Therefore algae will take advantage of this excess light and nutrients to flourish. The plants will then have only as much light as the carbon content lets them, which means low light. This seems to be the case in your tank, is that the plants are not nitrogen starved, but might be carbon deprived. But you don’t have high-light plants in your tank so that’s ok.
Elodea/anacharis are very hardy plants and they will survive fine that is why your tank is doing so well. So if you don't have enough CO2 (and you dont want to supplement carbon) it's not the end of the world, the plants will have to be low-or-moderate light plants and you might just have algae, which is not bad for your tank but is rather unsightly.
So don't get me wrong, I'm not discouraging an "over-planted" tank. My lab mate (he sits next to me at work) is a HUGE aquascaping hobbiest and even a judge in the Aquatic Gardener's Association (AGA) 2007 Aquascape contest. He uses hundreds of plants for aquascaping so I think the heavily planted look is beautiful. From him, I inherited tips on how to keep plants and tanks looking pristine (algae free, no decay, and full of color), but perhaps that is not everyone's goal for their axie tank and it’s not possible to have the plants’ AND the axolotls’ best interested in mind. I just wanted to point out to Markw that all but the hardiest plants need more than minimal care and he needs to consider a few things before diving into the (wonderful) world of live plants.
AGA contest I mentioned here
http://showcase.aquatic-gardeners.org/2007.cgi?&op=showcase&category=0&vol=1&id=6
So if you follow Oceanblue's lead and plant elodea (anacharis), anubias, or other low-mod-light, hardy plants and you will be in really good shape with low CO2 and low light. Again, commercial ferts are not recommended for the sensitive axies so dont waste money on them.
I didn't mean to scare anyone away from live plants, some of them are fool-proof and are worth planting for the aesthetics and nitrogen reduction.