Direct assay methods are easier to carry out, requiring only the one step to obtain the data. This could be studying a reaction that produces a fluorescent product in a UV-vis spectrophotometer, or using NMR (with slower reactions). The reaction is conducted in the observation cell, reducing the number of reactions that need to be completed, leading to fewer steps and therefore less room to introduce error.
Quenching techniques can be useful in faster reactions, allowing many samples to be produced at different time intervals. Using apparatus like a quench flow device allows faster reactions to be studied, which may not be possible with direct methods.
Quenching techniques are also able to be used with indirect assays. The product from the quenched reaction can be converted, making it easier to study with cheaper and more accessible equipment.