Every time someone tells me they spent their weekend 'dealing with' ivy, I feel like I can literally hear the silence of the missing pollinators. It is such an important late food source for all pollinators but will only flower on mature growth. While this growth does tend to be the bushier, heavier stuff that will bring down an unstable wall, it is also teeming with wildlife. So many insects and birds make homes in the nooks and crannies of the twisting arms that it seems an absolute crime to cut it back or chop it down. In the spring, birds and predatory insects like wasps and ladybugs are vital for keeping populations of aphids and other bugs under control without the use of pesticides so providing a home for them just makes sense.
So, if your wall (or, in our case, an incredibly ugly carport) can deal with the weight, please leave the ivy alone. And if you are looking for an evergreen climber that is brilliant for wildlife and also provides year-round seasonable interest, plant some ivy!