What information are you trying to protect?
If you are using one Apple ID, you can limit this ID to just App Store so you can have the same apps on the devices. However, if you enable other services (mail, contacts, calendars, etc.), then all devices get the same information. This may not be the ideal data protection policy. For example, if the ID is your primary Apple ID and you are using iCloud mail, then your employees will see your personal mail.
While your deployment model is likely working, there are fleet management solutions that can help manage the devices. For example, you can look into Mobile Device Management (MDM) solutions. There are many including (in no particular order) Jamf Now, Mosyle, Apple Business Essentials, and many more. For iOS/iPadOS devices, most any MDM that fits your budget will suffice. If you are planning to support Macs then Jamf Pro still crushes to competition. Some MDMs may even be free at your level of device count.
Please keep in mind that just because there is a better way to manage devices, it does not means that it will be beneficial to your and your business. As a child care provider, I am sure you are not sitting around thinking, "boy, I wish I could spend my day learning Apple device management." As a professional consultant, these concepts are easy and second nature. But, I will assume you are not an IT professional. If this is true, then the most effective may not be the most recommended.
If the Apple ID is a "general" ID meaning that no one person uses it all the time, then at your size, this may be the easiest way to manage your devices. You can license apps once and, if app install is set to automatic (Settings > App Store > enable App Downloads), the other devices will automatically download the app without user interaction.
Also, should you need to purchase an app, you can skirt the licensing rules and purchases it once yet deploy it to all the devices. If you were to move to an MDM with Apple Business Manager, you would need to purchase the app in volume (one license per device). If you has children who need communication tools like Proloquo, then this can get expensive, quick.
Regarding Family Sharing, this may solve for your current count. If I recall, you can add 5 uses to a family plan. If you were to increase the number of devices, you would scale above the capabilities of Family Sharing. Second, unless you are looking to provide each staff member with a unique Apple ID, then Family Sharing would not provide any benefit over using the single Apple ID to add apps to each device.
Hope this is helpful. Apologize for length.