What should SWAT do to help their cause? For starters, be professionals. Be your agency's indispensable, go-to, tactical specialists. Do what you do best, and do it every time. SWAT is best at handling high-risk, dangerous assignments. Work with, not separate from, your department's officers. Gain your entire agency's respect from top to bottom. This goes for everyone on your team, because everyone is a representative of your team.
SWAT commanders and team leaders need to figure out how, when, where your team can best support your agency. You're looking for that "just right" fit into your department's overall scheme. It's far better to be "too busy" than "not busy." Out of sight means out of mind. And this could very likely result in your team's downsizing, or perhaps its demise.
The bottom line is the more useful your team is to your agency, the less inclined anyone will be to delete it from the organizational structure. Especially in these uncertain times, it's always wise to try to anticipate the future.
Remember, law enforcement administrators are being increasingly forced to make drastic cuts, possibly including your team. The last thing you want to do is to do, or not do, something to make that decision easy.
From its inception in the 1960s, SWAT has continually faced challenges about its necessity. In the early years, SWAT was often viewed as a "nice to have," rather than a "must have." Given SWAT's sterling track record over its more-than-40-year history, I would hope every SWAT team has attained "must have" status within their agencies.