I do not think that this should be that much of concern, otherwise you are going to have to ban too much sounds. For example, adyghe language (spoken by 800 thousand people here in russia) has only two vowels, which are а and ы; russian, spoken by around 260 million, has 6 vowels (around three times less than german, i suppose). Mongolian (spoken by around 6 million people) does not distinguish b and v; it also has f sound only in loaned words. Turkish (spoken by around 90 million) has some terminal devoicing: at (“horse”) and ad (“name”) are indistinguishable (more or less); this also appears in russian (kod and kot are indistinguishable) and some other slavic languages, in malay language (spoken by around 290 million), in mongolian, and, as far as i know, in some varieties of german. And these are just some more basic troubles that someone might have with pronouncing randomly-generated words. Mongolian, for example, has vowel harmony, thus, for mongolians it is hard to pronounce a word that does not accord to rules of vowel harmony. You could possibly make a random word generator which creates words easy to pronounce for everybody, but:
- You will have to exclude most of world’s languages using some kind of criteria, e.g. exclude non-indoeuropean languages, or exclude languages that are spoken by less than 200 million people, etc.
- You will have to acknowledge the different phonological processes of all languages you chose.
But such a system will probably be just bland. I suppose you could instead use some obscure language with simple phonetics (such as hawaiian maybe, it sounds sweet and does not have much consonants). Other option is to choose some short list of languages according to your taste and only follow their rules.
Though i personally would like the opposite: making phonetics of random name generator as complex as possible. Maybe even making some obscure phonological rules (a foundation of the far-future mechaenetia conlang???).
Anyway, probably the best (at least from a value-to-effort standpoint) option is just use latin as a foundation.