Many of the above assumption are very conservative growth estimates. However, it is still worth noting that in order for this to work, Client A must stick to an investment plan in a disciplined manner. While many retirees certainly do just that, others have a tendency to panic during periods of market volatility which then undermines the above assumptions.
There are other variables worth considering such as taxes. If the funding source for the theoretical investment capital is a retirement account subject to income taxes on withdrawals, this must be compared with SS income which has some additional tax benefits. SS income is exempt from State income tax, and at least 15% of the benefit is exempt from Federal income taxes. While that is a slightly greater benefit for SS, it is not enough to offset the benefit of collecting early in many circumstances.