Sure, on has to do the sums, and for many people (unless they have night storage heaters) E7 will cost them more than would a single-rate tariff, for the reasons you mention.I have an E7 meter but a few years ago changed my tariff to a normal one and the two readings are added together for my bill. I worked it out and we were not saving any money on E7 as the E7 standing charge was higher and the day part of the E7 tarriff was more than a standard day tariff.
With most suppliers, one has to use at least about 35% of one's electricity at 'cheap rate' for it to work out cheaper. It's worthwhile for me, since I average 45% - 50% 'cheap rate' use.
Kind Regards, John