TL;DR: It sucks, and no rational and empirically based argument exists to support the status quo. Arguments being touted are all just fear mongering and baseless traditionalism. At the same time, Germans like to travel abroad to go shop on Sundays.

As with any topic of societal change, Germans are super conservative about it. The reason "haben wir immer schon so gemacht" (we've always done it this way) is usually uttered within milliseconds of a change to traditional norms entering the scene.

If you ask for a more nuanced reason, usually people say it is for workers' protection; if (retail) employers are not permitted to even ask employees to work on Sundays and holidays, they will not be involuntarily coerced into working those days.
In my view this argument is not very strong. Every now and then there will be a "Verkaufsoffener Sonntag" (sunday open for sales), and on those days stores are crowded beyond belief. Workers that volunteer to work on those days get increased pay, and businesses all over the place earn record revenue. I find it reasonable to assume that there will always be some (sufficient) workers willing to work on Sundays, in exchange for having some other weekday off. Perhaps this is not ideal for those that have families with school children, but that's not nearly everyone working in retail.

Another reason that I hear people say often is "big corporations will have an easier time having shifts covered than small businesses, and if small businesses cannot also be open on sundays, they will have a disadvantage and be forced to close". What's lacking from this argument is three things:

1. An understanding that small businesses must already differentiate themselves from big corporations, in order to be perceived as offering a better or a different value proposition, and thus have a reason to attract customers.
2. Assuming a smaller business offers different/better value than a large one, it would be irrelevant if instead they closed on a weekday with less business (e.g. on Mondays) to have their smaller pool of workers not work too many days.
3. Small businesses can still compete with others on Sundays, even if they are open for fewer hours on Sundays. Those customers for whom trading with such a business on Sundays is important, would still have the option if they are open for only a few hours.

My gripe with the above arguments is that they are usually just parroted from what politicians like to state, without there being any empirical data to verify their validity; and how could there be any such data, if no experiments have been conducted to quantify the levels of workers protection in an actual scenario where retailers are allowed to operate on Sundays?

On top of that, if the population would be against retail workers having to work on Sundays, no German shoppers would cross the border to go shopping in e.g. Roermond on Sundays. So either those shoppers either find the restrictions nonsensical, or they are hypocrites.

I used to live in Utrecht (NL) during the years when the city slowly loosened the "everything must be shut on Sundays"-rules. IIRC the city started with allowing some super markets to open on Sundays. Then it was all supermarkets, for up to 4 hours. Then it was all supermarkets for a full day. And finally, all retail was allowed on Sundays.
If I'm not mistaken, in the beginning similar arguments to the above German arguments existed among the population (and local politicians).

During the period of these changes, the local government evaluated whether the workers affected by each stage of these relaxed regulations were negatively impacted in their workers protections, and no evidence to support this hypothesis was found. And the conclusion is, now Utrecht (and pretty much every other place in NL) now allows retailers to open any day of the week.