I've seen experienced captains, FOs, load controllers, regulatory specialists, etc .. all make dreadful mistakes with loading systems .. and I include myself there as well, even though I have been designing and using the things for 30 years or so.
In general, and presuming a good level of understanding and training, the guy who is walking the walk the most is more likely to have a better control of mistakes. However, the fact that no system is foolproof leads to the normal QA requirement that there is an audit of the first run of whatever is being done.
With a trimsheet, this works well with the load controller (by whatever title) preparing the document, and someone else, normally either captain or FO (depending on the local rules) running a second eye over the document.
The problem with the computer generated form is that, typically, the output is not amenable to an independent check ... meaning that we are, to some extent, trusting our necks to the computer ... and a computer is never wrong, is it ? How you get around this problem is, in itself, a problem.
Over the years, I have formed the opinion that the "best" way is for the load controller (because he/she is at the loading coalface) to run a trimsheet, and then the crew does a joint check with the captain checking the numbers while the FO runs a trim check using, ideally, a circular or similar, slide rule style of trim adjuster.
As to whether the document needs a physical signature will depend on
(a) the rules as published, and
(b) the airline's procedures, as accepted and approved by the regulator. It may well be that there exists a concession or dispensation against the ANO requirement.