Do you consider it as a good (or bad) thing to ask them for their
self-evaluation? What could be the (positives/negatives) drawbacks?
Overall it's a good thing. But it does set some expectations. Make sure those expectations are clear and that you follow through completely.
Explain ahead of time what you are doing and why. Make sure you clearly communicate that you will be writing up the final review, but that you value their input. Make sure that you explain that it is your job to write the formal evaluation, not theirs, and that you are looking for their help.
Decide ahead of time if their self-evaluation will be filed along with your evaluation. And decide ahead of time if they will be allowed to formally comment on your final evaluation or not.
Some employees will welcome the chance to help you consider all the details of the past year as you prepare your evaluation. Unfortunately, these will likely be the employees who will be getting a "good" evaluation and a good raise.
Other employees will take this as sign that you don't really understand or value the work that they do and will attempt to use this self-evaluation as a counter to your critical evaluation or as a way to blunt the negative aspects of their work This group will include those employees who had "not really a good year".
Hopefully, you have a one-on-one meeting to review their self-evaluation in which you go over their points, ask for any needed clarification, thank them for their input, and remind them how the rest of the process will go.
And hopefully, you have another one-on-one meeting to review your final evaluation report. In it you can review the year including both what went well and what needs improvement. If their self-evaluation was very rosy and your evaluation wasn't here is where you need to be able to be open and honest with your feedback. This can be a difficult conversation - be very prepared.
Encourage your team members to keep track of their accomplishments throughout the upcoming year, to use as input into next year's evaluation.
Since at least parts of this process appears to be new, you may want to talk to HR about it before you start. They would likely have some guidance on how to do this effectively in your shop. They may even have some requirements regarding what you will be permitted to do and what you will not be permitted to do. Many companies have a standard evaluation process and wouldn't permit deviations.
You may also want to run this past your boss. Some bosses wouldn't want part of their team evaluated one way while the rest are evaluated a different way.
Think it all through completely before you start. And make sure everyone understands what you are doing and why.