I should have put it as "time travel", but it's as close to it as we'll ever get if the past and future indeed do not exist, only the present being what we have available.Redecorating a house was an extreme simplified example. But what you suggest is merely an extrapolation of the same thing. It's not time travel, merely making a model of the past - an accurate model, sure, but NOT time travel.
The reason people seek time travel usually relates to wanting the state of matter to be the same, in cases such as:
Wanting to re-live in a place that is now different / destroyed.
Wanting to see the stuff that was happening back then, for example, in their childhood or as a tourist wanting to see the way things looked and felt like in the past (this can just as well be turned into a virtual world, provided that we manage to simulate stimulus of each of the five senses).
Wanting to see the people that are no longer alive (or their pets, or an extinct species).
Wanting to avoid making a mistake / getting another chance (although this might be limited unless measures are taken to re-create those events accurately).
Who wants to go back in time purely to go back in time though? Time's more like a property, like dimensions anyway, or what ever to call them, but they are not material, they define a material. You could just say it's 1900 today and it would not count because the matter doesn't look the same as it did in 1900. What is time anyway? Isn't it a property (as in, something that belongs) of matter and where there is no matter (not even an observer), time becomes non-existent and irrelevant?
They say that the absence of an observer renders time irrelevant, but as long as there is matter, time would be relevant for frequency in the changes of matter. Remove the matter and replace with the observer, time again is still relevant because the observer (possessor of matter) can count the seconds / minutes / hours / days / months / years etc even though there is no other matter around the observer. (this of course neglects the fact that the observer could not survive in a place where there is void only).