I looked into this when we redid our kitchen last year, and honestly the payback timeline is the real killer. On city water, you're maybe saving $200-300 a year if you're aggressive about it, which means a $5,000 system takes 15-20 years to break even - way longer than most people stay in a house. The maintenance piece is real too, but it's not as bad as some make it sound if you're thoughtful about what goes into the tank.
The actual hack nobody mentions: before you commit to a full system, try a cheap DIY bucket approach first. Seriously, just keep a bucket in your shower during those first few seconds before the water heats up, or while you're washing dishes. You'd be shocked how many toilet flushes that covers, and it costs you nothing except a bit of discipline. I've been doing this for months and I can feel a slight dip in our bill - not earth-shattering, but real. If you find you're actually doing it consistently and hate the hassle, then you know a real system makes sense for your household. But most people fantasize about doing this for a week and then forget about it entirely.
If you do go the system route, focus on the simplest, lowest-maintenance option available rather than the fancy ones with sensors and automation. Simpler means fewer things breaking, and fewer reasons to skip maintenance that costs way more to fix later. The algae and buildup risk only happens when people neglect their filters or when soap keeps getting into the tank - use a lint trap on your drain, don't put anything sudsy in there, and actually clean the filter like you're supposed to.