Is there any correlation of a society's level of development, values, wealth, etc and using a pictogram/alphabet? For example ancient Egypt seemed quite advanced with math, construction, and astronomy but still used pictograms.
There are several issues with approaching such a claim, mostly having to do with how exactly we can categorize writing systems and levels of development.
It's easiest to define writing systems, so let's approach that first. To simplify things, let's use three categories. I'll use the term "logogram" instead of "pictogram;" pictograms look like the concept they represent (e.g. emoji) while logograms are abstract symbols (e.g. the "5" symbol has nothing to do with the concept of five). I also add syllabic writing into the mix, that is, scripts whose signs represent multiple phonemes (discreet sounds).
Alphabets:
Syllabic:
Logographic:
Here we see the first issue. Latin and related scripts are primarily alphabetic, but, as mentioned our numbers and other signs (&,$,@,+,=...) are in fact logograms. Mayan, Japanese, and Korean rely on both logograms and syllabic signs. Egyptian contains single-phonemes signs, syllabic sings, and logograms- where the heck do we put it? Theoretically Chinese uses logograms, but after centuries of use they start to blur the line between representing ideas and sounds. It's not quite correct to equate each sign with an idea.
Even if we were to have distinctly categorizable scripts- how do we begin to compare "development, values, wealth, etc." Let's reduce it to political systems. In 1000 AD Japan, both syllabic and logographic scripts are used. At the same time, the Maya cities use a script which combines both. Yet Japan is ruled by an imperial family with some degree of centrality, while the Maya live in competing city states. Competing city states? That sounds like classical Greece or Renaissance Italy! You're right! But those both used Alphabetic scripts. Let's take it to the modern world. Bolivia, Canada, and Kosovo all use the Latin script. Are we to compare these three countries in an meaningful manner? With so many diverse places using the same scripts, we can't even begin to draw comparisons between those that use the same "category" of script.... if such categories can even exist.