Weightlifting shoes have a whole range of benefits- increased stability being a big one.
Shoes with elevated heels will indeed make it easier to reach depth without back rounding. It is much safer and more practical to have a heel than to put a plate/board under the heels, obviously.
If you can afford to buy shoes, buy them!
Having the heels elevated will not in of itself make you raech a higher level of flexibility any quicker.
Squatting, heels elevated or not, does however improve you flexibility over time.
So, what the shoes will do for you is to allow you to reach a proper depth without needing to improve your flexibility. This has many benefits, the most apparent being less stress on your knees, and proper glute/ham work done in the squat.
Of course, you should still continue to to work on mobility for other reasons, but it will make your squat much more comfortable and less frustrating, I’m sure!