Signing a PDF on a website does not work

Unless I misunderstood you completely I don't know what you're complaining about.

Uploading an image of a signature or creating a wet signature on mobile is not how you used certificate based digital signatures.

It seems like you're confusing electronic signatures with certificate based digital signatures.

Browsers like the ones you've mentioned, provide the ability to use certificate based digital certificate ID authentication mechanism.

And no, public and private key encryptions, hashing algorithms, how to set this up is not user friendly. But that is an International ISO standard, not an Adobe Acrobat standard.

Besides, the problem is not on the Adobe Sign platform.

Looks more to me that the problem is on the subpar performance of web browsers to view and work with PDFs in general.

I wouldn't have recommended the Adobe Sign  workflow if it wasn't user friendly. 

The hardest part is not for the users, but maybe in what is required from them to obtain a digital certificate from a trusted certificate authority provider in order to  uniquely identfy each signer to that certificate.

Again, this is an International industry standard as defined in the Request For Comments published and constantly revised by the Internet Society.

If applying a finger signature, signing with a stamp image, or a wet electronic signature is what you were referring to, then it should be even easier to use with Adobe Sign.

You cannot use these methods on a signing field that is meant for certificate based signature.

And embedding an Adobe Sign form to your existing website is not the same as developing and entire CGI script that will reside in a web server (not embedded inside an Acrobat form),  to interface with the same field objects of the PDF that a user must fill in. That is double the work to achieve such workflow.

If you insist that that is the route you believe is the way to go, the user must also need Adobe REader or Acrobat, and if you're employing digital certificate-based signature , or even self-signed digital certificates in this workflow; you'll only be able to use the default Adobe timestamp server or the one you select as default with your organization to authenticate the signing actions at signing time.

You cannot use or have the ability to configure more than one timestamp server to use simultaneously.

With Adobe Sign you can indeed provide the users with more than one timestamp server , which supports environments where a user has multi-approving or reviewing roles.

But maybe you're right.

Perhaps you can point where in the Adobe Sign guidance it says it doesn't supports the methods you're describing.

You need to know that Edge, Firefox and Chrome all use their own PDF viewing software. Three different ones, made by Edge, Firefox and Google. They blocked Acrobat Reader years ago. So there's nothing Adobe can do to make signing work online within these browsers, except to set up an online service like Adobe Sign. 

You need to use Adobe Sign for this type of workflow.