Yeah, this split boom thing might work as "fat" dipole but probably not a very good one.
Perhaps the greatest challenge in antenna design is bandwidth.
Not going to happen.
If it were me, and I've done stuff just like this, I would use:
Tilted Terminated Folded Dipole (this is a pair of parallel dipoles made of wire connected at the ends separated by the appropriate distance for the frequency range, a terminating resistor in the middle of one and feed in the middle of the other, generally sloping in the air - this is for HF, useful for shortwave listening and up to perhaps 50MHz. It's not very efficient but amazingly wide band and quiet. It requires a balun to match to coax or use a parallel wire feed.
I'd use a discone or biconical for VHF and UHF. Because they can be quite large at VHF it might be wise to use a simple vertical or "ground plane" for 150MHz and then the discone for 450 and higher which would cover everything pretty well up to about 1GHz. A Log-Periodic Dipole Array is a great choice for wideband with directional gain. It has less gain and wider beam width than the Yagi but a "neater" pattern. The Yagi is a great beam antenna but has a very narrow bandwidth. However, building a log-periodic with ideal parameters for best performance makes them much larger than if you sacrifice and they get quite large too for lower frequencies.
A TV balun may not be a good choice (even for TV). Any such device has practical limits to its useful frequency range. In addition that style which looks like the molded plastic one's Radio Shack and others sell is a rather poor device. They are also impedance matching, in particular to convert a 300 ohm antenna to 75 ohm coax, a 4:1 conversion. If your antenna whatever it is is not 300 ohms then using this balun will not be good for 75 ohm coax. A Yagi (without a design to compensate such as a folded driven element or gamma match) typically has a low impedance, around 15 Ohms. Using a 4:1 balun to reduce that, ... that's a losing proposition.
WA0CBW brings up some good points. Harmonics can be useful, or as stated equally bad everywhere.
A naturally resonant half wave antenna for example will also work fairly well at 3 times the design frequency. At twice the impedance is way off. A 100MHz antenna will work at 300 but not at 200. It would also work at 33.3MHz but with reduced signal because it just isn't big enough. This is oversimplified but shows the idea.
A dipole is a directional antenna on one axis, in the other it's omni. So if you used a dipole in the vertical orientation you get omnidirectional coverage.