Zoat isn't using the speed force, Zoat is using magic.
Kind of a lateral move, since the Speed Force and Magic are both aspects of the Source in DC comics, but eh.
Not really? They may have the same origin, but how they act within a story is completely different. Magic, generally, has known limits and restrictions, as well as its own areas of strength. Takes a long time to learn, magic items can't be mass produced, depends on personal mana if you don't want to rely on an outside force, etc. These limitations give it an ability to drive a plot, because the audience can broadly predict what CAN be easily solved with magic, and what can't. Nobody is pulling abilities out of nowhere, so tension can be preserved.
Speed Force is almost completely undefined in terms of what it can and can't do. Broadly, the user can do anything if they mumble the words "gotta go fast" while doing it. Run through time, make lightning, make tornadoes, whatever. Pulled directly from the DC wiki:
Certain speedsters can use the Speed Force for more advanced applications such as time manipulation, energy construct creation, creating copies of themselves, or stealing/lending speed.
Conduits of the Speed Force who were gifted other powers instead of superhuman speed include: age manipulation, spacial-time mimicry, atomic inhibition, and process speed manipulation.
Half of those have nothing to do with going fast. If someone has a connection to the Speed Force, then they can basically pull powers out of a hat, and the audience has no ability to say that it doesn't make sense, because there aren't enough limits to what it can do. So tension is really hard to create, because we don't know in advance what the protagonist's tools are, and they potentially could just solve the plot in an instant.
Also, balancing opponents against someone who can move and react at superluminal speeds is basically impossible, if you want to portray your protagonist as anywhere near competent.
Can you give some examples. Currently I can't imagine anything to slot into "death-focused akin to suicidal thoughts or certain cult ideas, but not that".
Awareness of their own mortality, or the mortality of the world around them. Contemplation of people who have died. Depression, even aside from those with suicidal thoughts.