"would be increasingly" is correct and usable in written English.
You can use it when describing a gradual change in a situation over time. For example: "Traveling to the US for tourism purposes would be increasingly difficult if the current visa restrictions are maintained."
They would be increasingly propelled into a world system already clanking away at full speed.
He said health experts would be increasingly concerned as the time nears for the annual pilgrimage of Muslims to Mecca.
And Ms. Jacobovits said the New York and Connecticut markets would be increasingly vulnerable to swings in supply and demand.
We hypothesized that this would increase CT imaging which would be increasingly negative as the pressure to maintain throughput rises on busy days in the Emergency Department.
He predicted that the country's deep economic malaise would be increasingly evident, with greater poverty and unemployment in the new year because of the government's mismanagement.
"Obama was inside that cozy group now," Alter writes, "and it would be increasingly difficult for him to see beyond its borders".
Karl Marx prophesied that the workers would be increasingly exploited and made miserable and that these conditions would lead to the downfall of capitalism.
On January 28th Fitch, a credit-ratings agency, said that meeting regulatory solvency requirements would be increasingly difficult for all but the strongest British insurers.
But he said it would be "increasingly difficult in the years ahead to remain successful in the UK without success overseas too".
Lacking the cover once provided by Egypt, the Palestinian Authority would be increasingly isolated in its policy of dialogue with Israel.
Officials said recovery of the remaining bodies would be increasingly difficult since many had been virtually molded together by the fire's heat.
