If your invention is a physical thing - device, apparatus, system, machine etc. it is (essentially) defined by its structure. Something meeting the claimed definition while sitting in a shelf would infringe regardless of intended use.
On the other hand if it is a method or process (which might involve the use of novel or not novel devices) the use and outcome of the use matters.
Of course it makes sense to describe a problem and how your invention solves it. This form is especially important in patent applications outside the US.
In a method claim the particular steps to achieve some end result are claimed. An invention that can be applied in several ways might have different claims for the steps involved and the respective outcomes.
There are many uses for aspirin. A claim to a particular dose and regimen to reduce a headache would not prevent another from another dose and regimen to ward off heart attacks. If you invented both you would need two separate claims and, in this divergent example, two patents.
Either find a way to generalize the description of the steps and outcomes to cover many “use cases” or write distinct claims for each. You might aim at getting a patent that covers a few lucrative uses and not worry if some other uses remain out if your control.
Any use you disclose would be one unpatentable by others even if you do not have a claim that addresses it. In the US a follow up divisional application could claim those disclosed methods if filings were timely.
Regarding design around - if you have two uses of the core inventive concept and you solidly claim use A but not use B then people can perform use B. That is not designing around it is taking something you left on the table. If your claim to use A has unneeded steps or unneeded specificity in a step then it can be designed around by leaving out the step or modification of a step that does not significantly hurt functionality.