As the school is giving only salary to staff and auxillary staff but other expenses like water and electricity bill, Lab fee, Transport fee. . Etc. Is anyway cut down. Teachers and auxillary staff is paid only a percent out of the total fees collected. The parents have to buy new devices and additional data pack for the online classes to run from home, To ensure smooth interaction.
If we're talking about the regular educational institutions who are currently using the internet to continue their classes I would argue not. By this I mean institutions such as primary school and secondary school. At least if we're talking about countries in which these are state-funded through the country's social system. In cases such as these, Which I assume is what we're talking about here, I don't see any reason to cut back on tuiton fees. In fact, There would be an argument for increasing the fees to pay for the new infrastructure that has been erected in order to deal with our current crisis.
However, And this is a big however, If we're talking about extracurricular classes, Higher education, Specialised classes and non-state funded classes I do think there's a good argument for a reduction of a considerable amount in a lot of these cases, Not least of which pertains to the fact that these institutions can theoretically teach an infinite amount of students at the same time in their classroom without it turning into either a singularity or a global humanitarian crisis.
I chose no here, Simply because there was already a good argument for yes and because I believe we're talking about regular education here. Take from that what you will.