It also depends on the temperment of future Kaisers. It took several generations for the British to put their monarchs into the Box that they did, even after the Civil War and the Glorious Revolution (having two German speaking monarchs in a row who had little interest in actually governing England/Scotland/Ireland certainly contributed too), and a big part of it was just... being born into a system where you're not the voice of god, crowned by divine right, etc.
Tends to make you increasingly susceptible to accepting abrogations on your power. Compound that from generation to generation, and it's hard to believe that each Kaiser might find themselves with a bit less power as each one becomes more used to having less power and thus more used to seeing the throne cede some power.
I agree that it will be influenced by future Kaisers, I will still stand by all the other factors I brought up as well.
There is something about this line of thought however, that puts me off when used in definitive statements as it requires the assumption that A to B happen it will eventually reach Z but that doesn't always happen. just as it takes a few lax monarchs to set the precedent of non interference. The same can happen in reverse hell this is the case with wilhelm the II who broke the precedent that his grandfather set off non interference and the same precedent his father wanted to codify. Though to give my best prediction it may continue with kaiser Wilhelm II precedent as from my understanding prince wilhelm correct me if I am wrong was quite similar to his father though was quite less eccentric. With quite a lot experience within the military and administration in prussian ministries he is quite qualified. A capable and active kaiser would likely bolster the Kaiser's role especially being he was not as contrevesy prone as his father from eccentricity. Plus with a successful Verdun he likely has a much better reputation as is likely considered a war hero.
To clarify i just think from a legal aspect the liberalisation of the empire is not as likely though i could see complete codification and minor changes to adjust for reform in prussia, however, any broad stroke changes in powers or structure i highly doubt as trying to shift to a British system through legal means as mentioned would likely require rewriting quite integral and substantial sections of the constitution which would have many opposing such transition both because it would shift the whole point of the very important role the monarch plays as the balance for the various sections of government and it would be trying to challenge decades of success with such a system.
HOWEVER, if we are going with the assumption of precedent with lax kaisers I could see the traditions such as appointing the president of the reichstag reichskanzler which would set the precedent of increased participation of civilian. Though I would say this likely only starts happening in the 60's maybe 50's during wilhelm the III reign possibly later depending on wilhelm the IV who i don't know much about outside of his service and death in the wehrmacht but that i would argue that this doesn't really leave a solid tradition behind as it may be rather fragile. Though I would still bet on such a tradition forming especially as I suspect the Kaiser role takes the more intended role of the central pillar which balances the various facets of government. I would still love to see this along with what I talked about in terms of trading social rights and reform in return for maintaining political dominance
TLDR: i agree with u and even suspect a certain extent of liberalisation from precedent and tradition set by the monarch though legally it it is unlikely to change and the monarch is likely to remain a central and influential figure in a more authoritarian Government then otl Germany