Question : Would it be worth registering with a public health insurance provider while living in Belgium?

Of course, especially if your pay social security in Belgium because the compulsory state insurance not only offers reimbursements for medical costs but also work disability allowance (in case of illness, accident, maternity and paternity leave).

If you pay social security in another European country, you must be in possession of an S1 form or E106 form and have the obligation to register with a Belgian public health insurance provider.