I worked in a similar environment where we were expected to complete industry based certifications. Initially it all seemed like a great idea, but the implementation was quite onerous on the staff and rarely did the learning align with our day to day tasks.
The ultimate impact on staff was that this was an additional workload that consumed potential billable hours as well as personal time outside of hours. Any disruption to the home life of staff that you try and force from the workplace is going to have an impact, your staff will receive pressure from their families and friends, or your staff are going to try an maintain their normal social commitments and do the extra work on top, which can lead to poor performance back at work.
My first advice is that if you are going to try and manage their learning, then you need to find a way to make sure it doesn't spill over into personal time. Any direction from you (management) is work, we shouldn't be going to the gym or playing social sports with the company/management unless the company is picking up the bill for that time, mandated learning goes the same way.
Any mandated pressure from work that impacts outside the normal/expected office hours is a change to the original working conditions, such a change can be enacted, but it should be recognised as a formal change to the conditions of work and therefor a new employment contract should be negotiated. If not offered, some staff will eventually resign or their morale and performance will degrade to a point where you ask them to leave.
For optimal results, try to align the study with actual business tasks. That way you will also benefit from their expanding skill set but it lowers the overall impact on the employees.
If the learning does not align with the work, you MUST offer freedom of choice. Managers can mandate work, they have no jurisdiction outside of the workplace. If the learning does not correlate to the work, then all you should offer is support and time. Any request from management is simply a work request. If I sit down to do some reading or course work at home, if my wife asks why I am doing that and not spending time with the kids, and my answer is "Because my boss wants me to do this"... The polite response from her would be something like "If you're not getting paid overtime for this, you can do it when you get back to work."
If you allow paid office time to complete studies but it is not aligned with their work, then you will realize more success by leaving staff to utilise that time as they see fit. Some might use this time to complete overdue projects or to otherwise catchup on billable hours, which for you is still a good option, but it would indicate that the rest of your management style does not align well with your offer of encouragement of personal growth. If your staff don't take that time to do something for themselves then it is likely that some other pressures in the workplace are conflicting, for instance you shouldn't set a quota of perceived effort to earn the personal development time, it needs to be condition free if it is to work, you might find that some people simply need this time to decompress or de-stress.
I find this to be the ultimate test of workplace satisfaction, if staff are eager to work on their own projects or learning and can demonstrate a level of productivity during their personal development time, then it can show that the pressure of the workplace is not negatively affecting their mental state. If they take this time to sleep or apparently do nothing, then this might indicate issues with their overall workload. If they continue to do work, however well natured they may seem about it, it shows that your emphasis or commitment to this personal development time is not reflected or projected by the rest of the management team or other business priorities.
To increase adoption, one avenue is to offer financial compensation, either as a lump-sum bonus payment or increase in salary at the completion of a certification or course. This is a clear way to both recognise and award the effort, but also to demonstrate your commitment to actual outcomes. The carrot is there for motivation but it helps with staff retention, once they are more qualified, then they could easily seek higher paying roles elsewhere.
Sometimes, we get those members of staff who are simply not interested in putting in extra effort. That has to be OK, we are all managing our own work/life balance. Some of us might like the idea of personal growth but simply not have the motivation to do anything about it personally. Maybe they have achieved that perfect balance or are simply happy with where they are at in life, it is not for us to judge them or to force them outside of their comfort zone, to do so would often lead to negative impacts on work.
As they say, "You can lead a horse to water, but you cannot force it to drink".