If you use a rooting type of algae it could take over and you will never be rid of it. This can be a problem.
Floaing algae like chaeto doesn't do that well in tanks since it moves around.
Some fish will just destroy it - even if they don't eat it. I had a gunea fowl puffer that would just chew up nori, chaeto, etc. and spit it out.
Also keep in mind that you will need near reef quality water for algae to thrive long-term. I am not talking about just low amounts of PO4 and NO3, but also adequate trace and major minerals/elements. If you grow calcium based algae, then your calcium/alk demand will be very high. In regard to the NO3 and PO4 levels, the algae alone will likely not be enough to keep the water completely low on PO4 and NO3 so you will have to lower stocking levels, change a lot of water and get a huge skimmer.
It can be as much trouble as a reef. If anybody has ever had a freshwater planted tank, then they will know what I am talking about.