Digital signatures are sometimes allowed in the U.S., but, when they are allowed, they are allowed only in the context of a fairly specific statutory procedure for doing so.
Part of the idea of a manual signature is that a human being manually writing something creates an original document that can be pulled out if necessary and has some rather distinctive aspects to it that can be examined to see if the signature is a forgery. But, in contrast, when you cut and paste a signature into a document, there is no way to know if the person doing the cutting and the pasting is really the person identified in the signature, even after the fact with forensic expert attention.
Another part of the idea of a manual signature is that the physical act of putting a pen in your hand and putting it on a physical piece of paper is a time honored and traditional way of symbolically giving assent to what it on the paper. This physical act is what legally constitutes your consent. Indeed, it isn't even terribly important for this aspect of the idea that it be your name. The practice of having illiterate people write an "X" on a signature line with the intent that they will be bound is used for this same purpose, even though it is probably not identifiable forensically (although it rules out a signature by a literate person). Tapping keys on a keyboard that cause a copy of a signature to appear in a document is arguably not distinct enough from other kinds of keyboard use to make it stand out from the other actions of a person to make it a distinctively symbolic act of assent in the way that a manual signature is distinct from simply typing or writing prose.
Indeed, the importance of this manual signing activity in conferring the significance of important legal actions is memorialized in a group of statutes collectively known as the "statute of frauds" which says that certain kinds of legal acts are only legally effective if they are in writing and "signed" by the party against whom the document will be enforced. A cut and paste of a signature, even if authorized by the person whose signature it purports to be, doesn't count as a signature for statute of frauds purposes, unless legislation specifically authorizes that and the legislation that does so has limitations and safeguards built into it.
The important part is not that it is digitized -- photocopies and electronic reproductions (such as scanning and faxing) are often allowed in lieu of originals. The important part is that the signer engaged in a distinctive, individualized symbolic act to authorize the matters set forth in a document by the conventional manual means or a statutorily approved alternative.
Of course, cutting and pasting scanned signatures is a very new thing under the sun. Mimeographs were expensive and were not considered individualized assent signatures either. Before that, the recognized and valid alternative to a manual signature was a seal, often in wax. But, seals fell out of favor before they were replaced with digital cutting and pasting.
We are still in transition. This transition is particularly hard certain documents that are "real" as opposed to being mere evidence of your intent, such as checks and promissory notes and wills where a photocopy is not considered to be equivalent to the original. It has been accepted practice to allow faxes of many kinds of contracts to be considered valid for 30 years or more, but allowing people to deposit a "real" document like a check electronically has only been possible for a few years.
Sooner or later, this requirement will cease. But, it will take time. Consider that for almost a thousand years, in order to validly sell real estate, the seller had to physically hand some dirt from that location to the buyer in what was called the "livery of seizen". A couple of hundred years ago, we finally dispensed with that tradition and let a signed and notarized deed take its place. The complete transition to digital signatures will no doubt happen sooner. But, we aren't there yet.
There are several "uniform acts" proposed as models for states to adopt on the subject such as the "Uniform Computer information Transactions Act", and the "Uniform Electronic Transactions Act", and the "Uniform Electronic Transactions Act", but these have not been more or less uniformly adopted by the states.
There is also federal legislation on this subject in the U.S. called the "E-Sign Act" (formally the "Electronic Signatures in Global and National Commerce Act", 15 USC § 7001 et seq.) adopted on June 30, 2000. The E-Sign Act authorizes but does not require businesses to accept digital signatures, prohibits states from favoring one E-Signing technology over another, and contains some consumer protection provisions. It exempts wills, codicils and trusts, divorce decrees, separation agreements, and foreclosure notices, among other kinds of documents.