Why do some guyed broadcast towers come to a point at the base. It seems that it would be more stable if each vertical bar was anchored separately rather than being balanced at one point.
If the base of the tower is "rigidly" fixed to the ground, the foundations have to withstand the bending moments from the side loads (e.g. wind) on the tower. Otherwise, the foundations will work loose and not support the tower at all. Depending on the local geology, that may mean deep foundations to support a tall tower. Foundations are expensive, because unlike the tower itself they can't be prefabricated to a standard design off site and delivered by truck!
By using guy ropes and a tower base as shown, the only force on the foundation is downwards, and if the foundation gradually sinks into soft ground over time, that can be compensated for cheaply by adjusting the guy ropes.
The tower can be in a location of extreme winds or temperature change. Or it may be located at a point where there is interruption in direction of cables.
Wherever the reason, there is anticipation of excessive stress on the guys and demand for flexibility at the bottom to allow the tower freely deflect with the expansion and shortening of the guy cables and not experience undue stress.
In such cases if the tower were to be self standing on its own legs, it would be necessary for the guy cables to counter undesirable resistance of a self supporting tower to tilt it into optimal angle. Here is Wikipedia link guyed tower