You can rent an appartement for a flatrateprice indeed, but when the owner gets the electricitybill someday he will either raise the rent for it or kick you out ;-)
Also most leases have a clause in them about "not running a business" in your unit. The electric bill plus an inspection of your unit will quickly provide all the evidence the landlord needs to sue your ass (and/or confiscate your entire security deposit) for breach of the lease contract.