Hello,

We have been blessed and can typically afford to fly priority/ First class and have always been able to board prior to the main cabin...

What happens if we are not there when they call on FC passengers?

Do we wait in line with everyone else or do we cut to the front and show our FC boarding pass?

Some policies and gates are setup so a lane is reserved for FC/premium pax to board at their leisure.

Sometimes it becomes "converted" into general pax lane, after the priority call.

So if it's there, I take it. If it's not, I wait in line. When theres a dense crowd crowding the gate and I'm in no hurry, theres not much to be gained fighting the masses to assert my right to board. It's a nice perk to have but isn't going to kill me if I don't don't have it.

May as well just jump in line as soon as you get there; after all, there were probably people trying to cut in during FC boarding anyway...

Your correct, sometimes they do convert them to genaral pax line.
But that makes sense. If it is there, take it, if not wait...

There is no general answer to OP's question. What carrier, what airport, and even what gate.

While the carrier really matters, the latter may affect the practicality of the policy's implementation.

AA, by way of example, if it has two lanes available, will always have one of the lanes for priority passengers. If you arrive after Zone 4, you may still enter the priority lane and the agent should call you forward by unhooking the tensor blocking it. If there are only a few people in the "general" lane, it seems not worth it. But, later in the process, when the general lane becomes full, your ability to use the priority lane means less time in line and seems quite worth it. That, of course does not work at gates which lack the space for two lanes.

Other carriers vary, but the general principle is that "priority" means "priority".

We typically fly with AA and Delta. Always depart from LAX.

I rarely fly Delta, so can't opine on their process/procedure.

However, with American, there's usually two lines - one for Priority passengers (not just First class) and one for everyone else, by group numbers. However, it can be quite a mess, especially at the onset of general boarding. If you can make your way over to the Priority lane, I believe they'll take you at any time during the boarding process. Sometimes I've seen them rope off the Priority lane, but I don't think that means it's closed. I think it's just to keep general boarding in one lane. If you come up to the Priority lane and indicate that you have a First Class seat, they'll usually open it up for you.

Don't cut lines proclaiming your status unless you really want to show up in one of the many DYKWIA threads on Flyer Talk.
(Alternatively, you could hire a sedan chair and bearers along with some young girls running in front of you spreading flower petals and shouting "Make way! Make way! A Status Flyer approacheth!" )

Most, if not all of the Delta gates at LAX now have the "boarding zone pylons", I believe. There should be a several posts in the boarding area (sometimes they are mobile and the gate agent doesn't put them in place till just before boarding begins). Each post has a boarding zone on it, which corresponds to the zone on your boarding pass.

In my somewhat limited experience, when I have arrived later in the boarding process and stepped up to the Premium pylon, the GA called me to the front and scanned me in next. I can't say that it was always worth it though, because after that I was in the same line as everyone else, creeping down the jet bridge to get on the plane. based on those experiences, if I can't board with the Prem zone, I will usually just wait till the end - since it doesn't take any more time than standing in line.

If I arrive after first class is called and the economy passengers are swarming over the premium lane, I just approach at the side so my boarding pass can be seen and the staff usually notice and call me through. I don't wave my boarding pass around like I am so important. Please and thank you go a long way.

A few years back we went to the priority gate at Schiphol, unaware that they were operating a pen-like system. The GA swung a gate which effectively stopped an economy pax who was legitimately passing through, dead in his tracks with a barrier in front of him, to allow us to pass through.
It was quite embarrassing to my wife and me and I decided that if a similar sheep-pen traffic system was in operation on subsequent flights, I would rather go to the back of the economy queue.

Do not wait with the dregs. Go directly to the front of the line. Display your boarding pass. Enjoy the glares of fury from the long queue behind you. Watch in amusement as the gate agent drops what they are doing to the dismay of the lower form of animal life they were helping until the moment you arrived. Ignore anyone who lips off as if they aren't speaking the same language. Stride purposefully on to the aircraft secure in the knowledge you paid mightily for the privilege of being at the front of the line. Once settled in your seat have a champers. You've earned it.

Great to see all these perspectives on the OP's question.

I do apologies in advance for jumping in, but I'd like to cheekily throw in a question of my own

Given you know that the people are not in the correct group, how would you handle people blocking the way into the jetway/document check when priority boarding is called? Will you barge in or wait?

Granted, this isn't a question that is valid in every airport (esp. those with priority lines), but rather those employing a pen like system (Kuala Lumpur and Jakarta in particular comes to mind)

The use of the term "barge" suggests going somewhere you are not wanted or expected. So it wouldn't be "barging" to go directly to the front of the line and present your documents. Preferential boarding is a privilege extended to passengers by virtue of ticket class or status. You either earned it or paid for it and there is no reason to deny it to yourself other than some misguided sense of social conformity.