DaVinci Resolve's noise reduction does work, but you need to layer your approach rather than rely on a single tool to get clean audio without that processed sound. I had this exact problem with some outdoor clips last year - lots of wind and background chatter - and found that combining gentle passes with specialized software gives way better results than cranking one setting to max.
Start in DaVinci by using the Fairlight page's noise reduction, but keep it subtle - use the De-esser or the Noise Reduction module at maybe 20-30% strength rather than aggressive settings. The key is multiple gentle passes look more natural than one heavy-handed one. Then export just the audio track and run it through a dedicated tool like Adobe Audition (if you have Creative Cloud), iZotope RX Elements, or even the free Audacity with noise profile removal. These programs let you isolate a sample of the pure background noise and subtract it more intelligently than general plugins can.
If you want something faster and less manual, there are AI-powered options now that do a solid job - Topaz Gigapixel Audio or similar ML-based tools can reduce noise while preserving voice/dialogue clarity pretty well. The trick with any method is A/B comparing before and after on good speakers or headphones, not just trusting what it sounds like in the editing timeline. Most phone mics pick up way more ambient stuff than we notice while recording, so don't expect perfection, but these layered approaches will get you 80% of the way there without that robotic hollow sound.