With a phone, some maid may plan to runaway. That's the biggest issue with Indo maid at the moment. The agency is just trying to make sure the maid don't have modes to plan her runaway.

2nd, it's all about trust. Does a phone makes a maid productivity drop? Yes. Always based on what I see.
But lay down ur rules. Talk to her nicely that you have said the phone is being place at a certain area so that she can use during emergency but it's not for her to keep.

At a certain point of work years, you may relax it and let her keep it. It's like a reward system based on trust.

Not all maid are the same. Some have pretty good education background like they study until Form5. You need to know your maid more, like how's the family and etc. Understand what's their needs and not just yours.
Indonesian maid now are not like 20 years ago (unless you are getting from really kampung area).

Remember your priority - take care of baby. The last thing you want is baby masuk hospital because of long term feeding bad stuff.
For me, productivity is 2nd priority if maid is home alone with baby.

My maid was with me for 8 years before she when back after the 1st MCO. We had stealing incidents after 6mths of working. Shouting incidents in between my wife and her due to house chores. Bad attitude after 1 years plus. Each time, we deal with it immediately (not punish yeah). But the difference is my maid was educated (can even read basic English).
Once trust is establish - u can go dating with your wife again and starts to enjoy ur own hobby.

Trust your gut instinct.