10? Try 5 years or less- the mentioned 'generation' from source material. The best example we get of training rates is Aiden's sibko . . . and by the time they are in their final years there are less than 10- I want to say less than 5- cadets still in the program. When they test, its only him & Marthe- or was there another pair? A single (or three?) warrior graduated from a original decanting sibko of 100.
I used percentages to demonstrate losses and replacements for the simple reason, its not about the absolute numbers but the flow. The pipeline pre-Invasion and before disasters like the Jihad would be to simply maintain the status quo number of warriors give or take a few. The Clans before the Invasion, and even since, do not fight many multi-galaxy battles. The whole point of the bidding system is to decrease the amount and numbers while protecting the infrastructure for damage- if you can win with a cluster, why can't you win with a trinary if the opposition scales back the same way? If you want to expand your forces, you logically start planning that 5-8 years before if you want to relax the standards (look at the Vipers, there is peer pressure against that solution) or you start 19 years before you want to expand . . . which is usually longer than a single Khan's term. Even with their higher washout rate, the Vipers still funnel the final failures into supporting arms.
The Refusal War was devastating for the Falcons, not only in the equipment lost but in the man power. Read the summaries, a lot of the Falcon units were gutted taking for IIRC something like 70% material losses and over 60% personnel casualties. Some notes had all the Aero or Elementals wiped out from the cluster and they lost enough clusters in that Trial to form even 6 or so of the larger Falcon galaxies. The future Warden Wolves and Kell Hounds alone wiped out two galaxies (13? clusters). Ulric & Natasha took down 2-3 clusters on each of the worlds they hit before Wotan which gives you something like 10+ clusters conservatively and more likely 14 or 15 total. The ONLY thing that saved the Falcons post-Refusal were the hidden sibkos, and Marthe still graduated a lot of them early to fill slots.
The Clan sibko system is engineered to maintain a certain force level. I doubt we will ever see a product that describes why, but some sort of even must have occurred to freeze them into their pre-Invasion strengths otherwise they could have built huge armies. The ONLY source we have for changes in a touman's paper strength would be the Coyotes who declined though no reason was ever solidly established for such a drop in strength.
As far as freebirths . . . yeah, the Jags did not use them. They were also quite arrogant and while I agree with the fiat argument is valid its also irrelevant since the whole BTU is built on fiat. Other Clans refuse freebirths AND have stricter programs but still managed to recover from their Tukayyid losses (Vipers!) though you could say their being thrown out of the IS indicates their weakness . . . it was against the Falcons right after the Refusal War, they should have been stronger. Not sure anyone else has that bias.
While a mechwarrior will take longer to train that a grunt infantryman, it will not be that much longer . . . they just will not have the skill of Clan mechwarriors. They basically graduate the sibko as veterans having been operating mechs for 6-8 years by that point and been in combat. Part of that is related to their warrior emphasis while the IS trains soldiers. For example, I think tank crew take . . . 5 or 6 months to train in the US Army- 3 months Basic, 2-3 months MOS school. In war time that 3 months of basic would be cut down to maybe 2 or 2.5. Freebirths still go through a longer process than that if not the testing from birth trueborns experience.