Wouldn't work. The first thing the dictator does is to abolish all three houses. And if he doesn't have the power to do that or all kinds of other things he shouldn't be able to do in order to have the same effect then he has no point in his position existing in the first place.
There'd be no need. The general idea would be to have the Dictator interfere only in logistical matters and to keep the country from falling apart. All the politics would be handled by the Houses.
And the Dictator would have all the power he could ever want anyway. He'd pretty much just be able to sit around on a sunny beach somewhere being blown by a harem of slave women if he wanted. All he'd be doing by dissolving the Houses would be increasing his workload and making himself a target.
So you just make sure the first Dictator is smart and selfish. Then he doesn't care about using his power to conquer the globe or build huge statues of himself while the people starve, as he'll be perfectly content to sit around sunning himself.
Essentially, it remove the Dictator from the consequences of his actions - so he can't really improve his life by being a dick and he can't cause himself hardship by imposing 'for your own good' things on the populous.
Plus, he'd still be one man. And men can be
dealt with. The only way he could usurp power anyway would be through the military, and they'd already have a large degree of power by way of the Second House. And even if they did try to take power, half the Second House would be billionaires would could scupper their plans, the entire Third House would be patriots opposed to the idea of a coup and the First House would be full of regular, selfish idiots who would be clamouring to maintain their own power.
It gridlocks the system if anyone tries to seize absolute control.
So while the Dictator could do whatever he pleased on a personal and state level, if he tried to combine the two the organizational structure of the government would mean he'd be trying to take power from the Military, captains of industry and selfish, manipulative politicians. He'd be dancing in a nest of vipers.