"greatly impede" is a perfectly correct phrase in written English.
You can use it when talking about something that is significantly and substantially slowing down or hindering progress on a task or activity. For example, you could say, "The broken tools in the machine shop greatly impeded the fabrication process."
The tax breaks for nuclear would "greatly impede market access for competing energy sources," Mr. Koplow said.
Residential and commercial roofs, roads, and parking spaces for automobiles greatly impede the absorption of water into the soil.
These extreme cuts and changes would greatly impede the nation's economic recovery, and hurt those on the middle and lower economic rungs who suffered most from the recession.
"Our delegation had come convinced that if the Port Authority, the owners of the towers and the city were still liable, it would greatly impede the building of downtown".
However, the complexity, strict environmental requirements, and/or high cost greatly impede the applications of these techniques.
However, the complex curing procedure (high temperature and vacuum) and limited hydrophilicity (∼90° of wetting angle) greatly impede its functionalities.
All these factors have greatly impeded the country's economic development.
This has greatly impeded a more general appreciation of Bellotto's whole oeuvre.
Such lack of immunity greatly impedes our work helping those in need as well as in reporting their stories to a wider world.
But after 10 weeks, an unspoken obstacle is greatly impeding a settlement -- the growing hostility and distrust felt by both sides.
Moreover, addition of a small amount of sulfur in various forms makes the rubber molecules sufficiently irregular that crystallization (and, hence, hardening at low temperatures) is greatly impeded.
