My chlorine is kept very low, but yes I keep the cover on all the time-- well except when we go swimming (he he he!) I partially agree with you on the fact that you will gain more solar heat with the cover off during the day. However, your net energy flow will not be better by doing that as you will greatly increase the rate of water evaporation with it off and as we all know evaporations will very quickly cool the pool. So, I strongly believe you will better off to leave it on all the time except when swimming.