1. You can borrow money via secured loan by using the plane as an asset, allowing you to take out MUCH bigger loans. You also pay much less on insurance and will see higher profits since you aren't paying weekly leasing fees.
2. The benefit of paying off loans is having a credit line you can use if sh*t hits the fan and you need money. In Beginner's World you won't have to worry about it, but in regular game worlds you'll have fuel spikes that cause many airlines to BK. Thus, if you have a $100mm plane you can borrow against, this helps out greatly in managing your finances.
Also in terms of gaining airline value, when you pay $300k towards a lease it is gone forever. If you pay $300k towards a loan you secured with an aircraft you own, you're company value will go up $300k (well not go up $300k--it just won't go down $300k).