As you stated, it is not recommended. What make/model are the drives? This will let someone hopefully provide you some feedback on if these are problematic or should survive. In reality, you have a warranty on your drives. If you always plan for the drives to only live as long as the warranty, you will be safe because if the drive should fail before the warranty, you can get it replaced for free.
If you are going down this path I would recommend you have high redundancy.
Buy very good quality parts, Power Supply, Motherboard, RAM, you get the point. If you buy cheap you will likely pay the price later and pay it hard. Remember this one thing, your MB, RAM, CPU should last the lifetime of your system, well over 10 years. If you have an UPS, your power supply will likely last as well.
I do not know what your use case is for the this NAS but if you wanted a quiet system, that can be done using M.2 or SSDs vice spinners. If you have some case fans making too much noise, you can lower the voltage to the fans to slow them down. If you are using SSD/M.2 you might be able to get rid of most of the case fans. This means some good planning on your part.
No, you can power your system up and down every day if you like. It is not recommended but you have a warranty on the drives. Plan to replace them at the end of the warranty and if they last longer, BONUS POINTS!
Why may a drive die faster you ask, it's the current the spindle motor used to spin the platters up. Everytime you power up the drive it induces this extra stress. Now some people "sleep" their drives and are fine. It's basically the same thing as powering of the drive and back on. It's a way for them to use less power and in some places, that can make a big saving in power costs.
Good luck.