Should languages keep historical artifacts?
Three examples :
American English have lost the u in word like "color", because it is closer to its phonetics (the u is silent and there's no particular sound associated with "ou"). The letter u has an anglo-norman root.
Swiss French (and for this particular example Belgian French) differs little from standard French, apart from the numbering system. It is ironically more metric than standard French since it streamlines what's left of the base 20 (vigisimasomething) system, i. e. it's "seventy and eighty" ("septante et huitante*") instead of "sixty-ten and four-twenties" ("soixante-dix et quatre-vingts". Historically people all over the world used some sort of base 20 system, probably because we have twenty toes and fingers.
*no one ever use "octante". Belgian people think the Swiss uses it, while Swiss people thinks the Belgian it. I don't know why its that.
Swiss standard German (not dialect) have ditched the Eszett ligature (ß) in favor of a more simple "ss ". That ligature was more common in the middle age.
With those example in mind, do you find value in the "old" vs the "new" way of writing?
(in other words: spelling reformer partisan and opponent : what goes through your mind?)
Ok, so first I think it's important to highlight one thing, that writing is something quite distinct from language. Or at least that is it a very specific and definitely secondary part of what language is.
So I guess you are referring to writing in this case, also because I don't think other aspects of language can be considered historical artifacts even if they've been present for a long time or appear only in some dialects. I believe both keeping historical marks in writing and getting rid of them have their pros and cons.
If you keep them, linguistic "archeology" is easier, you can go back in time and learn about how things were pronounced in the past or how different languages are related to each other. A fossilized script can also help with homonyms, as in Chinese or even in English, where different words are pronounced the same way but written differently (of course this only helps when reading, especially when reading without context, which is not that common).
On the other hand, if you get rid of these quirks, you get simplicity and compatibility. Compatibility is less important today that we have computers that can generate and read any character (like the ß you mention or Chinese characters), although they might still cause problems in other situations (computer filenames, official documents, etc.). Simplicity, I think, is the most important aspect here. Reducing the effort needed to learn a script is, in my opinion, totally worth it. Learning the Chinese or Japanese scripts can be a long life nightmare for a foreigner and, to a lesser extent, to even native speakers (check character amnesia). But also English or even French orthography is pretty old fashioned and not very reflective of current pronunciation. Getting rid of these things also shortens the distance between spoken language and written language, and since spoken language always comes first in natural languages (except for sign language, but even then signs come before writing), it is an easier path.
So, from my point of view, simplification and modernisation of orthography is mostly a good thing. The biggest problem it faces though, is romantic attachment. People get used to how they write words and go crazy when there are any changes on the convention (mostly because of lack of linguistic knowledge, starting with not distinguishing between spoken and written language).
The numbering in French seems rather silly and difficult to get used to (for a learner) and I find no value in that. Things like colour or Eszett don't matter that much.
So I think there's two aspects of this question. Firstly I think there's no debate that studying history is always beneficial - history of language is no different. Learning what words used to mean and how they used to be used lets you understand their present meanings better and use current language more effectively. Also it's interesting.
Secondly there's a question about whether you think language should be prescriptive or descriptive. Should the dictionary tell you how a language works, or should how language works tell the dictionary what to write? I'm very much in the latter camp where usage trumps all but I know some people, and even some languages (French and Icelandic spring to mind where they have 'official' boards who make up new words) prefer the former.
Vaguely related, I had a great discussion on reddit a while ago about the meaning of the word 'meat' and whether that will ultimately encompass lab-grown meat or even non-animal meat-like products (such as Impossible Food). Given the track record of English for borrowing, reusing and mangling words, I'm fairly sure that 'meat' will come to mean rather more than it currently does.
German is both a fantastic argument for and against this I think. On one hand, the various spelling reforms over the past few decades have created multiple generations of people who spell the same words differently, which makes an already large and complex language even messier. From what I hear from my mother and grandmother, they've caused more harm then they fixed, although I don't think I'm qualified to give a personal opinion on the matter. I can say it's certainly tripped me up a few times. On the other hand though, German is filled with quite a number of archaic systems like the counting system pronouncing ones before tens, the grammar is filled with exceptions, and my god there is zero consistency with the genders. When "table" is feminine and "little girl" is neuter, you know you've screwed up... :P
So I think ultimately it depends on how it's carried out. Ideally you want a gradual but continuous transition, and you want to get it as straight as possible the first time so you don't have to keep changing the language.
There doesn't need to be consistency between grammatical gender and things with real gender, grammatical gender is just used for case markers and what word is assigned what grammatical gender is mostly arbitrary, see here and here for a more in-depth discussion.
As an aspiring linguist, I love these kinds of things. Every language has them, in one way or another. For instance, Japanese kanji are great, I love them, but yeah, they create a lot of complications, especially now, as the world becomes more and more computerized. I think, with time, more and more of these features will disappear as more people have education and more obscure rules are forgotten (in recent memory, who vs. whom).
Languages are evolving all the time, and we can't change that. We should only save and cherish the old forms, the old scripts and recordings. No need to modernize the language, no need to stagnate it either, people will change it on their own. Later, people like me will go to old internet to learn old dialects and try to decipher them as we deciphered Shakespeare.