It's what we are used to, but it's not a priori 'normal' that verbs inflect for person and number - or indeed for anything. Proto-Indoeuropean did inflect for person and number and that takes a long time to disappear, so that's what most languages familiar to us still do. For various reasons, English is particularly progressive in many respects and has lost the inflections. But sooner or later it will acquire other verb inflections. The example of French shows how that works, because there it's happening right now. So let's look at the history of French. Some of the details may not be completely right as I didn't look up anything up. It's only the general idea that matters.
Classical Latin: canto.
The verb has the first person singular ending. If you absolutely want to stress it's the first person singular, you can use a personal pronoun. In the course of the centuries, with increasing frequency people did that even when there wasn't a strong reason to stress anything. Ultimately it became normal to say:
Later Latin: ego canto. This is redundant. We have a pronoun and a suffix, which both give the same information about person and number.
As everyone already knew the person and number before the verb suffix was even pronounced, people pronounced it more and more sloppily. At the same time, the personal pronoun ego, being used so much, gradually acquired a simpler pronundation je.
French: je chante.
There is little person/gender information in the verb suffix, and it's not needed because this information is already in the personal pronoun. The personal pronoun definitely doesn't automatically feel. like it carries stress any more. And definitely can't leave it out any more.
As a result, a new personal pronoun emerges that can be added to indicate stress:
French: moi, je chante.
In some cases (not this one - yet), the normal person pronoun is contracted with the berb.
At this point in the development of French, ignoring the spelling and history but only focusing on oral French as it is used today, we could say that French verbs are inflexted on both sides and that the empathic pronouns moi, toi etc. are the real pronouns of French. The suffixes will disappear more and more, until French verbs are marked for person and number by a prefix rather than a suffix. For example like this. (The example is not phonetically plausible.)
Implausible but illustrative future French: Moi jchante, toi tchante, il/elle lchante, nous nchante, vous vchante, eux lchante.
Why is English almost finished with suffix shedding? Why does it look as if German has hardly started?
English branched off the German-Danish dialect continuum when people from around the German-Danish border moved to Great Britain. The various constitutive languages were mixed in a natural process in which nobody tried to make the result behave like Latin. Some who were originally speakers of Celtic languages or of French were also involved. The result was a rapid simplification.
The other Germanic languages have been a bit slower with some changes, and German much slower. For a long time it was just a dialect continuum, not a standard language with dialects. The endings got simpler in each dialect, but I guess in different dialects this happened differently. When scholars wanted to create a written language standard (17th-18th century), they were not interested in simplifying the inflections, but in making them as similar to Latin as was possible by picking suitable endings from the various dialects. The result was a standard language more conservative than all the dialects.
If you compare the recent history of German and Dutch, you can get the impression that German is changing much slower because standard Dutch updates when the dialects change, whereas German doesn't. It seems that for most Dutch speakers, standard Dutch is an averaged dialect, whereas for most Germans, standard German is an almost unchanging standard which dialect speakers learn like a foreign language. That's why the endings haven't started to disappear in German yet.