Many have built models of the Eiffel tower with toothpicks too, so?
You can still built things with inadequate tools: inadequate != prohibitive. You just have more problems going forward.
Which is exactly the lesson people who write large scale software have found.
What is this "just about every bit of software we all use everyday" that you wrote about as been written in weak types?
Most major software is still written in C/C++ (anything from operating systems, Photoshop, DAWs, NLEs, UNIX userland, MS and Open Office, databases, webservers, AAA games, what have you). One could use just that C/C++ software, and they'd have almost all bases covered.
The rest is e.g. Electron based software and online services. For the latter, most of the major ones (e.g. Gmail, Apple's iCloud services, Microsofts, online banks, online reservations, etc, etc) are not written in "weakly typed languages", only the client is.
And those that were initially written in a weakly typed language, e.g. Twitter with Ruby on Rails, others with Python, etc, have rewritten critical services (or entirely) to statically typed languages (e.g. Twitter went for Java/Scale, others for Go, etc).
And even for the client, most shops are now turning to Typescript (and FB to Flow) because they've found weakly typing is not good enough for large scale. So?