Portugal’s animal crisis: Should we be euthanasing newborns?

Hi, I am a resident in the Eastern Algarve. I have 3 rescue dogs and 3 rescue cats, most of them already a bit older (the eldest I have since 2014).
I cannot even look at all the requests on Facebook, I feel so sad for the animals that are waiting for a home…
I am going to say something that maybe people find a wrong thought… But it would probably help solve the problem a bit.
When a pregnant dog or cat is found and brought to a canil, would it not be better to only keep one of the newborns, and euthanise the others in a gentle way?
Because if you do the math, and count the totality of all newborns in canils and imagine that lots of  them can (and will…) reproduce in the future, when finally found a home/,or back on the street again, then the older dogs/cats that have been waiting in the canils much longer, will have almost no chance to be chosen for adoption.
If all the pregnant dogs and cats have all their puppies & kittens in the canil and they all need a home, then it is just never going to stop, there are just too many cats and dogs in the waiting list.
In my opinion, the older dogs and cats deserve a better chance of finding a home, but that will only happen if the amount of cats and dogs in canils can be reduced. So that is why, instead of bringing up all the newborns, I think that a different policy (euthanise the newborns, but keep one) could help.
It may sound as a harsh solution, but how many of the newborns that are now all brought up will really have a good future ahead of them? Some of them will end up on the street again, they will reproduce… while so many older dogs and cats are waiting in the canils to be adopted…
I really think that by euthanising newborns in a gentle way, we avoid a great real of future suffering AND it gives a new future to so many other older animals.
Kind regards, (name and address withheld)