I had a baby who just refused to nap; from very young (around 2 weeks), her awake times were much longer than recommended for her age. A few times during the first month, I did feel like she was awake longer than she should be but I hadn't done any research on baby sleep before I had her - I had lots of help from family members who have raised children and was happy to take their advice which was to follow her cues. I tried this but she didn't used to show any obvious signs of tiredness (no eye rubbing, turning away etc). She did however, do long stretches at night from 3 weeks (starting at 4-5 hours and increasing to 8-10hours by 12weeks).
Up until I sleep trained her at 5.5 months, she did not nap well (if at all) during the day. The few times she did would usually be a 20ish min catnap and that would often only be once in the day so total 12ish hours sleep in 24 from 3 months old. We did go through a stage of managing to get her to nap in the pram after walking outside for 2+ hours but that was not consistently successful and an injury meant it was not sustainable on a daily basis.
Like with you, taking her to bed to nap would result in her chatting and playing, then crying when she realised I wasn't playing with her and wanted her to sleep. Rocking would have a similar result and same for everything else we tried. The biggest difference between my situation and yours is that she would get grumpy, cranky and overtired - by this point, she was so far past tired that she was pretty much wired and putting her to sleep was impossible.
When she hit 4 month regression and stopped sleeping at night plus also still wasn't napping, I had to do something. I was terrified of the impact of such little broken sleep on her long term brain development. She was also getting so overtired, she was practically inconsolable but still would not sleep. We used a sleep consultant who put us in a typical 7-7 routine, initially with 3 naps which dropped to 2 by 7ish months. I followed the routine to the letter for the first 2 months, staying at home for most naps and only deviating if I absolutely had to. By doing so, I've learnt so much more about her, how she shows that she is tired (she has completely different signs to any other baby I know), when she wants to sleep longer or stay up.
Part of the sleep training included us firmly establishing sleep associations - now we have succeeded in showing her that it is nap/bedtime and going to sleep is not negotiable, I can move her timings around if necessary. We also don't follow 7-7 anymore, it's more 8-7ish (waking for a feed once) with around total 3 hours daytime sleep.
She will still resist sleep if I give her the opportunity - I've accepted she will always be like that but with the right associations, she also goes to sleep happily without protest now and I feel so much more confident in knowing what she wants.
From my NCT group of 8, only 2 of us follow a routine so clearly not essential but for my circumstances, it has made such a big difference and she and I are so much happier the way things are now.