It's can be very useful in specifying exactly what is required in terms of compound and dose. The traveller may be able to give coherent and accurate description, but the pharmacist and/or doctor will be reassured by a written prescription.

This is particularly important in situations where drugs not available off the shelf can be dispensed on a discretionary basis by a pharmacist. (I've got to admit I have no idea if this situation holds in Thailand).

The prescription could also be useful in validating the traveller's entitlement to carry pills/syringes/liquids at customs/security.