Well, let's just get things straight:
Supply side economics is usually not just "let's give money to a certain group of people" but rather usually seeks to cause changes in behavior in the populace, the reduction in marginal tax rates is usually partially understood to be an incentive for these people to work more by giving them a greater amount of the wealth generated, it also can be understood as a means of causing accounting manipulation to be less desirable, as such is costly to the economy and to the user of accounting practices, so by reducing taxes, we can reduce the use of this sort of accounting. Now, of course, the issue with tax rates on income is that there are income effects and substitution effects, and it is argued by some that the substitution effects work against the effectiveness of tax decreases in generating greater productivity. However, in other matters, tax decreases can cause greater levels of growth, such as I think research has come out positively on the matter of decreasing taxes on investment returns leading to higher rates of investment, and I think that the stance that corporate taxation is inefficient is also not unpopular either.
In any case, the aim of supply side economics is usually to create better long-term growth, which is why supply-siders will usually want like ideas such as dynamic scoring models, which determine the changes in GDP caused by supply side actions, and this emphasis on the long-term is what separates supply-side economics from Keynesian "demand-side" economics, which focuses on creating a short-term manipulation of demand. Now, to be honest, supply-side economics has rarely been popular in the academic mainstream, and the few intelligent defenders are likely misrepresented by the politicians that use their ideas. For example, increases of deficit spending actually *work against* the desired growth effects that the supply-siders seek, but increases of deficit spending are what people usually see when they hear "supply-side economics". In any case, it is also somewhat unfair to label supply-side economics purely in terms of trickling down, because that represents the economy as mostly being benefited by the flow of money, however supply side economics does not seek to increase the velocity of the dollar so much as increase supply.
As for the criticisms of supply side economics, the matter of "hoarding" or "sitting" on the money isn't so much a problem, as unless the rich have a giant bathing pool for their money, in a Scrooge McDuck from DuckTales fashion, then they won't sit on it so much as invest it. The matter of spending it on themselves though is a valid criticism, as supply side economics mostly seeks to increase capital and labor in the economy, so if the determinants of economic growth are unaffected, then supply side economics fails.