It depends entirely on what you want to use the data for. If you are wanting to verify the chemical formula of a single analyte and therefore also make a stronger claim for the identity of said analyte then direct infusion is perfectly fine as you only need an accurate mass. There is no difference between a synthesized compound, a metabolite or a protein/peptide inthat regards.

But if you are working with a complex mixture and aiming to identify or tentatively identify a number if analytes of interest then you would in most cases be better off using LC-MS. You can still use direct injection in some cases screening out interesting analytes but for stronger identification out of a mixture you would want to try to separate them out as much as possible.

The LC-MS provide separation of compounds proor the MS stage, i.e. you can obtain a separate spectrum for each of analytes.

I think this is one of those definitions that has become to mean something different depending on your field.

In chemical synthesis ( where the term was probably used first ) Direct infusion would have originally involved a solids probe and an EI source. This gives a spectrum of a pure compound with many more fragments and therefore you can get structural information. When you introduce an interface that can do separation eg GC or LCMS /ESI then direct infusion becomes to mean, without a column. With an ESI source this simply means using a syringe pump or, for automation, an LC system without a column.

Your choice of DI-MS for pure chemically synthesized compounds is the correct one, you should be looking for a service that provides High Resolution ( sub ppm or =/- 3 mmass units at least )