The problem is getting the wires soldered on, even with a helping-hand holding the wires the gap between the solder joints is very close and joint does not feel secure.
The gap only feels small because you're out of practice, but your instincts about the connections not being very secure is right. That kind of connection is really bad for "real-world" use, where you need
strain relief and the ability to grip the connector, not the wire.
But, for building a project where the connection will be more-or-less permanent, and the parts are mechanically connected so there's no great strain on the wires, they're fine. Similarly, for hobby uses where you won't be doing a lot of (dis)connecting, there's a reasonable trade-off between the much
lower cost and needing to take a little extra care.
If you want to improve strength, you could use small pieces of stripboard or protoboard, and solder both header pins and the wire to them. That would give you the equivalent of a "connector shell" to grab, and the option of adding strain relief by using a larger piece of board and gluing the wires down.