I wouldn't underestimate the influence even just one informed juror can have on the outcome of a case. Maybe you won't convince everybody—true. But as a juror, you never know who else is on the fence until you voice your doubts and opinions. Some people are reluctant to speak out or deviate from the group, but will respond if somebody else is there to take the lead. Some people might even change a vote just to speed things along because they don't actually care about the outcome. You don't know what power you have until you try, and It's always worth trying.
According to FIJA (the Fully Informed Jury Association, which is a good resource for jury nullification information and support), a hung jury is functionally "far better for the defendant than a conviction. Undoing a conviction is very difficult. An appeal is not guaranteed in the first place. It may not be legally permitted, the defendant may no longer have the financial resources to mount an appeal, etc. Even when a defendant is able to appeal a conviction, that individual no longer enjoys the presumption of innocence." So if you can't nullify, hanging the jury is better than nothing!
Mistrials only mean the whole thing CAN happen again—not that it WILL. If a trial ends in a hung jury, the prosecution will usually review the strength of their case and weigh that against their existing caseload, budget, staffing, etc. to decide if it's in the state's best interest to call for a retrial (there may be some exceptions, but this is generally the case in both the USA and the United Kingdom). Sure, plenty of cases get retried. But in some instances, a mistrial from a hung jury can lead to the prosecution either offering up a more lenient plea deal, or—if they decide pursuing things is ultimately a waste of their time and resources—simply dropping the charges altogether (this is sadly common with sexual assault cases; they're more difficult to prove in a court of law, and while I'm obviously wary of false convictions overall, I do have tremendous sympathy for victims who end up with no recourse for justice once the state drops all charges). In short, you never know what the outcome of a hung jury will have on a case until it actually happens.
Even if the prosecutors do decide to bring a retrial, according to professional jury consultant Alan Turkheimer, "acquittal rates in criminal trials are significantly higher after hung juries than during original trials." So even if you can't nullify a jury, you might nudge things in the right direction overall.
So yeah, I would still argue that actually being on a jury is a thousand times more useful in the fight against wrongful prosecution than getting yourself immediately dismissed by soap-boxing during jury selection. We need more justice-minded people to be jurors (and/or magistrates)!