What problems might arise from making the runner-up in the presidential election the vice president?

The obvious problem was the one that provoked a Constitutional change. Two people with strongly opposing views ran for president. One of them won by a narrow margin and the other became Vice-president. The vice-president thus became a constant voice of opposition in the capital. And- suppose the president had died- suddenly the government would change- the new president would want to replace all the high-ranking Cabinet members- all of the president's initiatives would likely be scrapped and the government would be in turmoil. Indeed , there would be an incentive for an opposing party to remove the president if they lost the election.