The phrase "avoid the inconvenience of" is correct and usable in written English.
It can be used when discussing ways to prevent or mitigate difficulties or problems in a situation.
Example: "To ensure a smooth process, we should take steps to avoid the inconvenience of delays in shipping."
Alternatives: "prevent the hassle of" or "eliminate the trouble of".
The courtiers of modern tyrants have sought to avoid the inconvenience of death by creating new hereditary monarchies.
People with cellphones and laptop computers, they said, will be willing to pay extra to avoid the inconvenience of rundown batteries.
Should this really be sacrificed so that London second-homers can avoid the inconvenience of Sunday afternoon delays as they head back to the Great Wen from their Cornish getaways?
New York's garment manufacturers began to move their work to Chinatown in the nineteen-seventies, in search of stable low-wage labor, so they could avoid the inconvenience of sending work to Hong Kong or the Caribbean.
"Google Baby" — which derives its title from the practice of finding potential egg donors online — gives us no Upper East Side trophy wives choosing surrogacy to avoid the inconvenience of weight gain and relinquishing of gin and tonics.
The publication of The Catcher in the Rye moved Salinger's career into a new phase, though the writer was not there to witness the sensation that accompanied it, preferring to spend the summer of 1951 in Britain so as to avoid the inconvenience of interviews, public appearances and reviews.
Each day this week has felt like a Sunday in Boston, with streets largely empty as people stay away from the city's center, both to avoid the inconveniences of the security and because the security measures have limited where they can go.
And the best way of avoiding the inconvenience of pubic hair-laden bars of soap is to use the advertised booking service which will guarantee exclusive possession of the facilities at the house you rent for your holiday.
As well as avoiding the inconvenience of regular hospital trips, the single dose should avoid potential damage to organs such as the heart, lung, and oesophagus - which is a risk during radiation to the whole breast.
