I can't speak to the specifics of the artifacts at Palmyra. However, I think it's worth pointing out that your question kind of assumes that the ultimate goal of history is collecting facts and then putting them into books. This is sort of the version of history that is usually taught in US high schools, but it is a rather simplistic and I'm afraid to say impoverished view of the field of history.

History is much more of a dialog between past and present. Researching, weaving that research into a narrative, making an argument about it, and putting into a book is certainly a rough approximation of what historians are doing. But the field is not static and is very dependent upon theories and methodologies that will continue to change over time themselves. Therefore, we will never reach a point when we are "done" studying history and even if we've scoured every inch of Palymra, the loss to future historians is real regardless because they wouldn't necessarily have the same things to say about it that current or past historians have.

There are always new questions to ask, particularly in archaeology (where new scientific methods can open new fields of research, allowing future generations to do things with sites that previous generations thought were fully excavated). When artifacts, sites, and ruins are destroyed, our ability to continue to interrogate them with these new questions is limited, and we're forced to work off our records.

In the case of a well-studied site like Palmyra, it's not a total loss; we can continue to analyze the records that survive as we come up with new research questions. But there's no substitute for having the actual artifacts in front of you for some kinds of research, especially scientific analyses.

At the same time, archaeologists always have a keen appreciation of the impossibility of perfectly preserving sites from the past. Excavating a site disturbs it, and - crucially - removes the layers of soil accumulation which preserve the record of human activity on the site. Archaeological excavation usually only has one shot to record a site, because after it's dug, all that important information in the soil that's been moved will only exist in the archaeologists' paperwork and photographs. Make a mistake, and you don't get a second chance. So archaeologists see sites destroyed every time we dig.

There's a constant tension, as a result, between the desire to know what's in the ground, and the knowledge that future archaeologists may hate us for not recording the information they need to answer their new sets of questions about our site when we dug it all up. In many places, it's become common to only dig sites at risk of destruction; otherwise, they can stay safely in the ground while our methods (like ground penetrating radar) improve. Even the artifacts removed from the ground can be damaged in storage - some things like wood and iron are very difficult to keep stable once they're excavated, and often decay unless there's adequate funding for expensive conservation. So archaeology is a tradeoff - information is always lost.

The wanton destruction of a site like Palmyra is tragic - I almost cried when they murdered the local archaeologist who cared for the site, and had no words when I saw it was demolished. We would like to have the ruins in the future, because they would make it possible to keep getting information from the site for generations to come. But at the same time, this kind of loss is a fact we have to accept, even while doing our best to minimize the harm our present actions cause to our herritage from the past. We can't put the past in a glass case, and - when even our best efforts to study the past harm it - well, what can you do but record as much information as possible so we have records of these sites that will answer some of future generations' new questions.

I would approach it in terms of "what knowledge might have been lost had this happened ten or twenty years ago?" Excavation was still going on until 2010 - see the site of the Milan University-Damascus Museum joint project at http://users.unimi.it/progettopalmira/index.html . Discussing one suggestive find at http://judithweingarten.blogspot.co.uk/2010/02/unknown-god-of-palmyra.html, archaeologist Judith Weingarten ends poignantly, "We'll just have to sit tight and wait." Seems that's what everyone's doing.

We have no way of knowing what we don't know. We have no idea what we might have been able to discover had it been intact in the future. I'll bet those ancient proto-russians that tossed that wooden statue into a peat bog ~11k years ago would never have guessed we'd be counting stripped down ions to guess it's age.