Do you know that this diagram is used in many particle physics talks. It is a schematic representation of a class of Feynman diagrams, that is a way to represent quantum field theory computations in an easy-to-grasp manner ;)
Is there a chance that dark matter will not interact with standard model particles?
Yes, it is possible that dark matter interacts only gravitationally, and nothing more. In this boring case from a particle physics standpoint, none of the three ways we use to search for it would work. Gravity is too weak at the level of a single elementary particle (which is the context for current searches) to lead to any observable signal.
If yes, wouldn't it make more sense to rather focus on the particle acceleration going on in CERN instead of spending time and resources on the Xenon-1T detector experiment with lower chances of detecting dark matter?
If we have a connection with the Standard Model, then all three classes of searches are needed as they are in fact complementary. In configurations where some are weaker, others take over. As the where depends on the model (which we don't know), we need to be pragmatic and consider them all. In some sense, we maximise the chances.