There is already a conlang that kind of does that. In toki pona you can write the words in a set of pictograms (actually, there are several pictogrammatic writing systems, I'm referring here to the 'hieroglyphs' from the official book). As there are only 120 words, it's easy to have pictograms for all of them.
The only problem is what happens with other words. Names, for example. The toki pona solution is to select a hieroglyph whose word starts with the respective sound. This leaves some choice, as you typically have several pictograms available and you can choose a word whose meaning is somewhat relevant to the name. For example, Kanata (Canada) could start with the pictogram for kasi ("plant, leaf"), to link to the maple leaf; Nokisi (Norway) would start with nena ("hill, mountain"), etc.
Here you are using pictograms to spell a word, but it is easily conceivable to have a separate script for names and foreign words.
If the vocabulary of your language is substantially larger than toki pona's 120 words, you might not want to use pictograms for everything. In this case you could use them either for 'core' words (whether you define them by meaning, age, etymology or frequency), or it could be words that have no inflections (and thus don't change, eg function words like and and for in English).
In the end it's your choice how you solve this, but there are certainly some possible justifications for different choices that you could explore.