Yes, if you delete a field, it is automatically removed from the page layouts. But it is always better to keep those fields in the back-end for some time, before it is being deleted permanently.
As mentioned by you in your question, it would be better to remove field permissions, doing so, you won't have to remove fields from page layout as those fields won't be visible due to access restrictions.
If you wish to delete fields, below are the points that you should keep in mind. (Excerpt from this salesforce article)
- Before deleting a custom field, consider where it’s referenced. You can’t delete a custom field that’s referenced elsewhere. For example, you can’t delete a custom field that’s referenced by a field update or Apex.
- You can’t delete a field if that field is being updated by a background job, such as an update to a roll-up summary field. Wait until the background job finishes, and try again.
- When you delete a custom field, all of the field history data is deleted and changes are no longer tracked.
- A background process periodically runs that cleans up metadata associated with deleted custom fields. This process will affect the Last Modified Date and Last Modified By fields on page layouts, record types, and custom objects.