A fun game mode don't get me wrong but its definitely not perfected. I believe the problems lie with the randomness of the waves and the timings.
Randomness of the waves - its a bit annoying, 1 match you just have to kill a few crawlers, grunts and jackals and wrap it up with an easy boss battle (especially if you have a tank and have to kill multiple Ghosts) but then it all changes, next match you've got to deal with 2 Warden Eternals at round 2 when all you have are warthogs and a BR.
Timing - while the timer itself is there to present a challenge so it isn't too easy, sometimes its just not enough. Especially when you have all the other enemy's breathing down your neck it just becomes overwhelming at times. The respawn timer is just bull, having to wait half a minute to get back into the fray on the final round where you need all the help you can get.
Solutions
While the randomness isnt a problem and it fact brings variety and on the fly adaptation, the fact a boss can arrive at as low as wave 2 IS a problem.
Regarding the timings, I'd say keep the original timer but make it if you kill one of the bosses in wave you get more time as well as decreasing the respawn times especially at round 5 where the problem is more pronounced.
Yay or nay?
Yay.
Yay
Yeah I just hopped in after the "adjustment update" and expected firefight to be fun. I was wrong anything important in firefight that needed changing, like the three warden boss that camp in the back of home base, haven't been changed. oh well back to arena for me.
A thirty second timeout doesn't test our skills, it tests our patience. How can it really be considered a skill challenge if you can't play? I get that it's a penalty for dying, but instead of a disadvantage that enhances the play, it simply removes us from play. Combined with the spawn location issues, we get removed from the action for a large chunk of the later rounds with each death. It's telling us "don't play", because aggravation plus actually-not-being-able-to-play equals "don't play". Inaction is not valid element for an action shooter. Whoever thinks that it is should be forced to watch hours of footage of players waiting to get back into play followed by them crossing half the map to where the fight is. Or they can be exiled to make Roblox games for a month. Or take away their substances they use when testing that make thirty second bans seem like a good idea and send them to me.

Figure out some other way to punish us for dying that lets us play and challenges us. Take away our REQ energy and armor mods until we refill them. Bump us down a level. Don't let us use a vehicle for 30-60 seconds. Issue a specific challenge like get a beat down. Give the AI that kills us a power up or health vampirism. Just don't lock us out of the action in an action game.
I think certain rounds see ridiculous difficulty spikes. One example is the Elite Banshee Raiders on Urban. Yes they have moved it to a later round, but they are accompanied by normal banshees too, theu have regenerative health as well as shields and are a pain in the behind that they have a habit of concentrating fire on a single individual. This knocks us out of the fight that requires team work, meaning only a couple of players are alive at any time. Whilst not impossible, it's very rare any team I have played with have progressed past this round. Even if you spawn in a vehicle, it is gone in seconds