It is not about what the government is allowed to do, it is about what is technically possible. If eavesdropping is technically possible, it is bound to happen, and constitutional protections will not be much help. The NSA revelations should tell you as much: the constitution is only tangentially relevant to the day-to-day decisions at the NSA about who to spy on or how to conduct surveillance.
The reality is that laws can change, and that when we create systems that are technically easy to abuse, there will be people who push for the law to change so that the system is legally easy to abuse. The police are always look for more power, and if you have something like Lavabit, the police will want to have on-demand access to it -- and they will want to reduce the barriers to getting a warrant, or even remove the requirement to get a warrant in the first place (like, say, if the emails are older than 180 days). By having a back door inherent in its design, and by positioning itself as the gatekeeper for that backdoor, Lavabit invites abuse and its users were lucky that the founder is a man of principles.
The reality is that laws can change, and that when we create systems that are technically easy to abuse, there will be people who push for the law to change so that the system is legally easy to abuse. The police are always look for more power, and if you have something like Lavabit, the police will want to have on-demand access to it -- and they will want to reduce the barriers to getting a warrant, or even remove the requirement to get a warrant in the first place (like, say, if the emails are older than 180 days). By having a back door inherent in its design, and by positioning itself as the gatekeeper for that backdoor, Lavabit invites abuse and its users were lucky that the founder is a man of principles.