The A345/6 were arguably Airbuses least successful aircraft, certainly in terms of fuel consumption and A343 may actually be more efficient despite being older. How many A346s are still flying? I can't think of many (but haven't looked very hard). I also can't think of that many A343s flying but the economics may still make sense. The last post mentioned finance costs. The lower financing costs of older aircraft may well offset their higher operating costs. This will be largely depend upon fuel costs - the spike in fuel costs a few years ago lead to the early retirement of many B744. By comparison fuel was very cheap last year. It may make sense to operate an aircraft up to the next D check and then part it out. Also the A343 is a heavier aircraft than the A333 which whilst making it more expensive to operate than the A333 is an advantage when it comes to cargo. (The B748 had relatively poor passenger economics compared with other aircraft but was good for cargo - although I don't claim to be an expert.)
Its interesting that very few if any A388 which with their high passenger and relatively low cargo capacity are flying and most airlines have retired their fuel and maintenance hungry pax B747s (cargo is another issue). Otherwise they are flogging their all cargo aircraft to the limit & making best use of their pax aircraft on cargo flights.
A lessor that has not placed a new aircraft such as an A350 or B787 might have trouble placing it as airlines wish to minimise spend and will avoid capital charges by using existing aircraft - its an interesting area but I'm not a leasing expert.
One other factor is crewing. Although demand is down some cargo flights are flying with heavily augmented crew to avoid having to crew slip where there are quarantine issues and will need to operate the aircraft they have crew for.