I've seen different things said about respiratory illness and I am wondering, if hens recover and are ever after "carriers" will they lay? Why would you need to cull your flock if you are not planning to sell birds?
		
		
	 
Yes, hens that have recovered from respiratory disease can lay eggs.
Each disease can impact the laying hen's health, productivity and egg quality even if they recover.
Most all respiratory diseases make the flock carriers for life, with the exception of Infectious Bronchitis which can make them carriers for up to a year.
Let's look at Infectious Bronchitis as an example - birds can recover, but the virus damages the reproductive system.  As you can see in the photo below, egg shell quality is impacted.
IB is also thought to be a cause of Salpingitis (Lash Egg) in laying hens as well.  Reproductive problems like prolapse, Internal Laying, Egg Yolk Peritonitis, etc. could very well be common too since the reproductive system is damaged.
Egg looks appetizing doesn't it?
		
		
	
	
Ref: 
https://www.betterhensandgardens.com/infectious-bronchitis-in-chickens/
https://www.merckvetmanual.com/poul.../overview-of-infectious-bronchitis-in-poultry
Let's quickly look at Mycoplasma - this disease makes birds carrier for life.  It also damages the reproductive system.  Egg productivity and quality is impacted as well.  Eggs may look "normal".  This disease is one that is transmitted 
both vertically (into the embryo of hatching eggs) and horizontally (bird-to-bird, dust, dander, etc.)
MG is also a cause of Salpingitis in laying hens and likely the cause of other reproductive problems as well.
https://www.backyardchickens.com/threads/what-is-this-salpingitis-warning-graphic-photos.1136522/
https://www.backyardchickens.com/th...-dust-one-by-one.1270059/page-2#post-20420498
As you can see, even when recovered, these diseases impact the productivity of hens, also the quality of eggs and hatchability of the eggs they lay, not to mention their overall health.
A lot of people do treat bird that have respiratory illness and they keep a closed flock.  They are aware if new birds are added, there is a risk the new bird will become ill (the new birds are also considered carriers when exposed).
If you are a breeder, you show, you hatch/sell/give away - then culling would be a practical solution.  Starting over would be both costly and heartbreaking, but some have done it to prevent the spread of disease.
I have just glossed the surface to your questions - there's a lot of information here on BYC about disease.  If you google each illness there is even more information to be found.  There is so much to learn and something new to discover about these diseases, it's hard to keep it all straight.
Here's a link to get you started - List of common poultry diseases: 
http://edis.ifas.ufl.edu/ps044