My take on it. A leased line or dial-up connection has some or all of the same problems you point out. What distinguishes VPNs is access. For an attack to be successful an attacker needs motivation, expertise, resources, and opportunity. In a day and age were attackers scan the whole Internet for vulnerabilities the smallest amount of motivation can lead to an attack.
Expertise is also easier to come by now a days.
By using standards protocols instead of proprietary ones we actually make it easier for the attacks to gain expertise. But we do so in the hopes that the openly reviewed standard will actually be more secure than the proprietary one. This is the old full disclosure vs security through obscurity trade-off. Resources are cheap and plentiful. What we are left with is opportunity.