Drew,
It really depends on your climate. If i do any grafts in my zone (9b) after March and i don't protect them from direct sun exposure they start to cook and die.
The parafilm can't solve that problem and even seems to make things worse (the condensation inside the parafilm and the high temperatures literally melt the buds).

Don't forget that i graft them on rootstocks that are in the ground and, in some places, this time of year, temperatures can exceed 90 ºF easily (probably more inside the parafilm).
It's different when grafting a rootstock in a container that i can place in a more shaded environment.
In some grafts i use only parafilm to do the wrapping (folded to be stronger) except for whip and tongue. This graft really needs a stronger tie and i use natural raffia that i wet prior to using.
I found out that wet, this material is stronger than tape and much more versatile (rubber is better and can work for most situations but, for me, sometimes doesn't provide enough tension).
Raffia is also thinner than tape which also allows me to go over the lower scion buds and leave them uncovered so they can start to grow without problems, like in the following graft.

As i said, it also allows a stronger tension, which is most important when using large diameter scions.
When done correctly the tie allows the perfect adjustment of rootstock and scion and contributes to graft success. Even strong winds or birds landing on the graft can't take it down.
The only drawback is that you can't forget to cut it after 2 months (sometimes less with fast growing varieties) or it will start to strangle the graft before it breaks.
An example with a large diameter scion and rootstock. The end flaps stick out (almost inevitable with large diameter scions and this type of graft) so the raffia helps to keep them tight and joined until they fuse together.
Afterwards, i cover the graft with parafilm to keep the moisture inside and keep the rain water out.




In May-7:

Regarding the use of the grafting knife, i entirely agree with you.
A few years ago, i used a grafting tool but, with experience, the grafting knife is much more versatile (i also do chip bud grafts with the same scion using the lower bud that would be discarded in the whip and tongue).
The grafting knife works in any grafting situation, even those where the grafting tool will not work. But, for those that do not want to invest the required time in the learning process of using a grafting knife, and don't plan on doing much grafting, the grafting tool (a good quality one) can be a good solution.
Sorry for the long rant on your thread, Mahdi.