A student with a psychiatric diagnosis (and this is an illness, not an emotional problem) has a right to apply wherever they please. As with any illness, admissions does not discriminate. What they do want to know is whether treatment is effective enough to enable the student to attend and do academics at the level they need at that particular school.
When anyone writes about what a person with major depressive disorder should do in terms of college applications, substitute what is more commonly known as “medical” illness, since major depressive disorder is brain-based and essentially medical.
For instance: Would a person with asthma be advised to stick close to home or go to a less rigorous college?
A letter from a professional to the Disabilities Office will help get accommodations needed, if needed, and those can go a long way to support a student with any condition or disability.
If being homebound is a sign that depression continues to affect functioning, rather than limiting where you apply, I would wait a year and continue treatment.