It’s just not true. Elster is already electronic for couple years. If you know what are doing it takes 4 hours max. I recommend your friend to find good tax advisor if he/she is not capable to do it by himself/herself.
The uninformed bullshit by the person you replied to is the reason I typically don‘t comment on German topics anymore on HN. Alas, my Gell-Mann-Amnesia is strong and I read comments on other topics even though they are probably as little based on reality as these comments on Germany.
Elster is an electronic version of paper forms. It requires redundant manual input of information that is present on different sub-sheets of the forms. Like the paper forms, it requires input of information that the government already has. Filing on paper doesn't take more time than filing through Elster.
Also, it's not unlikely that the government is printing the electronically filed information in the traditional paper format to be able to process it the traditional way. (maybe not for taxes, but it's surely the case for some other processes.)
But I agree that "3 months" is probably the time required to collect information, not the time needed to summarize the information for the government. Some banks take a couple of months to send the required yearly investment income/taxes-paid statement.
Some information can be entered automatically in Elster, e.g. the information submitted by your employer. For people with simple tax situations, e.g. regular employee and no additional complications filing the taxes is pretty straightforward. It can be a bit intimidating if you've never done it before, but almost all the information you need to fill out will be automatically provided. You need to get your bank/broker statements and enter them as well, but those tell you exactly in which line you need to put the values.
There's certainly a lot of improvement possible, but for simple cases it's pretty easy already (if you've done it at least once before).
It's all relative. In the most simple case there is no reason (and no requirement) to file a tax report at all.
Adding information from the employer is data that the employer has already submitted. Investment data could be transmitted from banks to the tax office directly, instead it's paper, as it always has been for the traditional process. The only iformation that would require filing is such not created through parties that are transmitting data anyway. e.g. private loans, collecting rent, etc.
As soon as any information is required to be transmitted, all information is required.
It's a process designed for execution on paper put into a computer. It's not a process designed for full automation. If any private company would operate that way they wouldn't be making any money.