Wallace: Increased-mass-production or Generation ships
It is not confirmed anywhere why Niander Wallace would want reproductive Replicants to exist, but I have a couple of explanations.
Increased production rates
My first educated guess (and what seems to be a popularly accepted theory) is that he wants to scale up his mass production rates. If he were to manufacture breeding Replicants, then he could create Replicant 'farms', which would allow his organisation to ramp up the scale of the Replicant production hugely.
This could boil down to a few a few reasons:
They live in a world of scarcity, there aren't as much resources available to them as there are to us now. Perhaps they are limited to the number of Replicants they can successfully create.
This is re-iterated by the fact that Wallace mentions his limited production capacity:
Every civilisation was built off the back of a disposable workforce... But I can only make so many
Paraphrased from memory, and stated in the official trailer (0:14)
Being able to 'breed' them would greatly increase their efficiency as far as resource usage is concerned, given that all they'd need is the bare necessities of food, water and shelter.
Rules and regulations
Although we aren't quite clear on what he rules around Replicant production are, we know that there are definitely some. One of these could be the number of Replicants an organisation can create or even might limit the production to 'On World' only.
The ability to breed as many and wherever Wallace wants would again greatly increase their production capacity.
My second educated guess is that he wants them to be able to man (lol) generation ships.
Wallace is hellbent on 'conquering the stars'. He specifically mentions that he has conquered 9 planets, but is not satisfied:
Nine planets. A child could count that on its fingers
-Paraphrased from memory
He recognises the depth of space and how out of grasp the other 'stars' are, so seems to realise that he needs generational ships to achieve this.
Yes, he may not see the result of that endeavour, but he seems to see that as his legacy.
Tyrell: Perfection or Next level service
This whole thing of reproductive Replicants is a new development as of Blade Runner 2049, so there's no evidence that Tyrell intended any Replicants to reproduce, much less actually achieving it.
Having said that, Eldon Tyrell was obsessed with the perfection of his creations. He seemed frustrated that he couldn't prolong their lifespan in his dialog with Roy Batty in Blade Runner. It's not unrealistic to assume that he would want them to be able to reproduce and even had a prolonged lifespan.
Remember, Tyrell's motto for their Replicants was
More human than human
That wouldn't be true to Tyrell if they couldn't reproduce and live for longer than 4 years.
Given that Blade Runner 2049 has now established in canon that Tyrell did in fact achieve this success, I'd say the reason he wanted to do so in the first place was to achieve the perfection of his Replicants.
Next level service
Replicants are service bots. They are built for a purpose - either to work as cleaners, medics, sex or whatever type of service humans may not desire. It is only logical to try and provide the next step in any service, doing what humans can't.
Unfortunately, there are many humans who cannot reproduce, no matter how much they want to. Many turning to surrogacy or artificial insemination. Imagine if Replicants could be created who are clones of your sterile partner, but with the enhanced ability of reproduction. That would be a disruptor in the field of medicine and parenthood.
Wheels don't need to be broken
In some of these cases, humans don't need to know that Replicants can reproduce. In fact, no one, not even Lt. Joshi knew that there was one Replicant who could reproduce in 2049. Wallace's plans seemed only visible to his most trusted, Luv. Additionally, it seems that Wallace was performing this 'experiment' in the privacy of his quarters, with on Luv having access.
This whole illusion of control would remain valid so long as Wallace and Tyrell keep it as a secret, until they are able to release the information in a controlled manner.