There are several reasons why an employer would mostly like to pay for burnout recovery coaching:
1) legal obligation, mainly: https://www.arbeidsrechter.nl/aansprakelijkheid-schade-werknemer-werkgever-ongeluk (like after ‘work accident’) and the principle of ‘goed werkgeverschap’ BW art. 7:611, ‘good employership’
2) employer is controlled by UWV; in case employee writes to UWV sickness department PO Box 57015 1040 CT Amsterdam including his test results or a burnout diagnosis, UWV will check whether employer offers help, and if not: employer is fined by UWV and STILL has to offer the help/external burnout recovery coaching
3) just the positive reason that after burnout recovery, the employer has a healthy performing employee again, like he had just after hiring you. In the burnout recovery coaching you learn to cope IN A DIFFERENT WAY with your stressors, and your life in general, and, JOINTLY with your employer, you remove most important stressors that lead towards your burnout.
It MAY be that an employer doubts whether you can function again in ‘that’ working environment in that you became ill/burnout; in that case you can, jointly with UWV, convince your employer to pay you a) external burnout recovery coaching b) thereafter outplacement to find an working environment that ‘more naturally’ fullfills your needs so you will not become burnout again. This is called ‘spoor 2’. It can ask some convincing power of yours and UWV, but most and good employers agree to this.