That's an excellent and very practical question! The short answer is: it depends entirely on the specific bench and who manages the public space. Generally, it's not something you should attempt to do yourself.
Most permanently installed public park benches have armrests that are bolted or welded into place. These armrests serve important purposes: they provide support for standing up and sitting down, define individual seating spaces, and prevent people from lying down across the full length of the bench (a design choice often made by municipalities). Removing them yourself could damage public property, void warranties, and potentially create a safety hazard if the bench's structure is compromised.
However, the need for more open, flexible seating is completely valid, especially for wheelchair users, people with assistive devices, or groups who want to sit closer together. The best course of action is to contact your local Parks and Recreation Department directly. You can propose the need for more accessible, open seating options in specific areas. Many cities are actively working to improve inclusivity and may have plans to install "armless" bench models or benches with alternating sections that have and lack armrests to accommodate different needs.
Some modern, modular bench systems are designed with removable armrests for flexibility, but these are typically managed by facility staff. If you are purchasing benches for private property, you can absolutely select models with removable or no armrests from the outset.
In summary, while you likely cannot remove the armrests on an existing public bench, your inquiry highlights an important accessibility consideration. Advocating for diverse seating options with your local authorities is the most effective and responsible way to create a more welcoming and functional park environment for everyone.