As a fully grown adult with a full-time job, having a relatively small 2-3 hours to play haven during the work week makes taming more or less completely unattainable. I think the limited/random time frame you have to tame an animal could be changed to make taming a bit more convenient and accessible. Either an animal should enter its "fight stance" exactly 24 hours after being hitched/re-hitched to a training post such that the tamer can adjust their schedule accordingly, OR the fight stance itself should last 24 hours without decreasing the animal's progress such that the tamer can reasonably be expected to be able to domesticate the animal.
I do not feel that the randomness in the current taming process adds much of anything other than making animal husbandry much more difficult to access for people with limited time to play. If anyone feels differently, and believes that the random time frames for animal taming is important to maintaining some sort of balance, then perhaps there could be two separate types of hitch posts, one that allows the tamer to rapidly domesticate an animal with the current randomness, and one that grants a slower domestication rate with a greater emphasis on predictability.
I'm open to debate but I feel that removing RNG from the taming process would be almost completely uncontroversial.