Because part of non-establishment is the general concept of not establishing - of having no say in the matter, neutral or non-neutral. The government should treat a religious institution and a non-religious institution similarly - which means that the original religious memorial could be joined by a non-religious memorial, but the government shouldn't be saying that it's a 'bad religion' and needs to be taken down while a non-religious memorial or memorial from a different religion remains up.
Under your proposed rules, if someone painted a Latin Cross, a Star of David or a Pentagram on the Washington Monument, would the government be prohibited from removing this religious expression?
If not, can you explain how this is different from the Mojave Cross case?