Just one point, I don't assume that all asylum seekers are lawless at all, but it's also hard to deny the reality that, in facilitating people smugglers by buying their services, the channel crossers are involved in an activity that is illegal. That small point aside, OK, no, you're right. I don't want to see people in rubber boats in the Channel.
I would also add that this issue long predates Brexit, and in fact in terms of numbers peaked 15 years before the Brexit referendum. It has merely been driven to the point of dinghies by the effectiveness of the UK's border in Calais, facilitated entirely with the agreement of the French government, which, were it to be suspended, would automatically place the border back in Dover, and your solution would become unavoidable reality.
I think that if your proposal is to work, it would have to be accompanied by a complete overhaul of the Immigration and Asylum acts, not only to function far more quickly and efficiently, but to ensure that there is a robust system in place to deport failed asylum seekers immediately upon the result of appeal. I regret to say that the issue of the Human Rights Act/ECHR would probably have to be addressed too, as it has been clear for many years that the system we have now is very easy for failed asylum seekers to play, and that there is an entire industry devoted to helping them do so.
Although they have their own issues (most particularly with people who are deported simply returning and going through the entire process again), Germany seems to be far more effective at actually deporting failed asylum seekers, as I believe does France, and they do so within ECHR.
This is not uniquely a British problem, and is one that can really only be solved by international cooperation, if at all. I don't doubt that France is frustrated that Schengen permits migrants to transit into its soil en-route to their intended destinations, and its police forces periodically go to some lengths to vent that frustration on the migrants themselves, presumably under orders. The EU has been indecisive and ineffective. However, the bribes that it pays Erdogan are holding 3.7 million refugees in Turkey. Should Erdogan choose to show the EU the finger, which well he might, your solution is certainly going to be put to the test. As it stands the policy is already empowering thugs such as Lukashenko and Putin.
Anyway, as regards public opinion, I think you might be a tad optimistic. I'm happy for you to put your theory to the test, but forgive me if I don't join you on the campaign trail. I've chased enough white elephants already, and I'm running out of time and energy.