You have some of your data messed up. The PS1 was $199 before the N64 even launched. They both hit $149 in March of 1997. Also, the N64 was outselling the PS1 in the US because it was the new console on the market. However, the PS1 was never behind the N64 in total sales. The PS1 had a stronger launch, too. 800K consoles sold in the first 4 months versus N64's 500K, while launching for $100 more than the N64.
Sony didn't cut the price to match the GC, as it didn't really challenge their lead. Just like with the N64, when Nintendo was forced to launch at that price to compete with the $199 PS1/Saturn, they had to launch for cheaper than the PS2. Sony didn't cut their price til 6 months after the GC launched. At that point the PS2 had been on the market for a little over 1 1/2 years, it was just time to cut the price.
The PS3 was officially dropped to $199 in 2013, with the introduction of the 12GB Super Slim. The inclusion of Bluray was more to help them win the format wars than it was to match the PS2's success. A success, by the way, that had nothing to do with it having a DVD player. The PS2 helped DVDs get to where they are, not the other way around. DVD players were available for cheaper than $299 when the PS2 hit shelves. And were available for $50 a year or two later. It having such a high SW tie ratio also disproves this myth.
Anyway, I think this gen we can expect the PS4 to be more in line with the PS1's legs after the PS5 hits. So, somewhere around 20M-25M. A $149 Slim and a $249 Pro should help them get there. I also think the $199 PS3 did so little because we were so late in a longer than normal gen. The PS3 had been out for 7 years by the time it had hit $199. People were done with that gen and were begging for new HW. A $149 PS3 wouldn't have interested them at that point. I think if they could have lowered the price earlier, even with a normal gen length, it probably would have matched the PS1's sales. Definitely would have come close to matching its legs if the PS4 launched a year earlier and PS3 was $199.