Engineers and architects never did build things. Eeither profession traditionally provided design, construction administration or management, feasibility studies for implementation of particular technologies, operation and maintenance plans, and many other related services.
Some engineers are involved directly with construction projects, but mostly they provide quality assurance, or construction administration related work. Most people who become engineers are much like you; loved to build mechanical or electrical equipment, structures, etc.
In mechanical engineering school they usually have CNC machines and other machining tools so that students can design and build practical devices such as Sterling cycle engines. In electrical engineering school there are laboratories where students design and build analog and digital electronic devices, experiment with power systems, etc.
It depends on what they're designing. For something like an airplane, technicians and tradespeople put it together. They're not usually required, but there should be some electives in machining. And you will have to take at least a basic circuits class. And most engineering schools will have student organizations like model rocket clubs. robotics clubs, formula SAE car if you want to actually build some things.
But in the real world, who would you rather have putting your aircraft together: the engineer who took 1 class that spent 1 week teaching the basics of riveting, or the technician who spent several months learning his trade?
You are probably right, they don't build much anymore.,
Electronics engineers may build prototypes, but even that is not so easy nowadays since the components and tolerances are so small. That means the prototype has to be assembled by a robot and automated machinery, and if the engineer builds a large version, it won't work quite the same since the board and wiring are themselves components with capacitance etc. Given that modern CAD/CAM has pretty good simulation capability, you can go straight from design to production prototype without a test prototype.
Assemblers and Technicians (a.k.a. people with no college degree)
Mechanical and Industrial Engineers do take classes in Milling, lathe, welding, casting, laser cutting, and more. BUT they take those classes so that they can perform their supervisory and engineering roles in manufacturing environments. They use that knowledge to find quality issues and recommend the best manufacturing processes to use.
Mech and Industrial Engineers typically never use that type of equipment in the real world, but it is important for them to understand how it works so they can properly lead the assemblers and technicians that use that equipment.
My friend who studied Aerospace Engineering in the same school as me graduated last year. His work is mostly on the computer. He uses Solidworks to model 3D parts to be used in Boeing airplanes.
An engineer must have some depth of practicality, an ability to fit things, and a good vision on how his design can be brought up to reality.
I have started going to school for engineering but got into it because I love to build and tinker with things. I noticed when looking through all of the classes that I have to take that there are no shop (i.e. milling, welding, electronics) that are listed. After some research it seems like engineers don't really build things anymore just design and test. Am I wrong with this information? (I'm going for aerospace engineering if it makes any difference) I would love to hear from an actual engineer! Thanks.