Why must gene entrapping constructs be integrated into introns and not exons?
I don't know that they must integrate into an intron. It seems perfectly reasonable that they could also integrate into an exon, as long as the reporter is in-frame. There is obviously an element of chance in that, and so the advantage of integration within an intron is that splicing will ensure that the reporter is translated correctly. Intragenic regions are also more abundant in the genome and so insertion is more likely. They discuss the advantage of this design in the original paper:
Gossler A, Joyner AL, Rossant J, Skarnes WC. 1989. Mouse embryonic stem cells and reporter constructs to detect developmentally regulated genes. Science 244:463-465.

...ES cells permit selection for rare-occurring integration events, which allowed us... to design and use a &quot;gene trap&quot; vector. The vector contains the lacZ gene, lacking a promoter and translation initiation signal, inserted in frame into the homeobox exon of the En-2 gene such that a splice acceptor is placed at the 5' end of lacZ. Integration of the construct into introns of genes in the correct orientation should create a spliced lacZ fusion transcript and a functional fusion protein when the reading frame is maintained. Evidence for this came from experiments in which a construct lacking the 5' En-2 splice acceptor yielded 12-fold fewer lacZ-expressing transformants than the construct carrying the splice acceptor.

Exonal insertions by gene traps have been reported:
Song G, Li Q, Long Y, Gu Q, Hackett PB, Cui Z. 2012. Effective Gene Trapping Mediated by Sleeping Beauty Transposon. PLS One 7.

Insertion of a trapping cassette into an exon or an intron of transcriptional active loci can generate a fusion transcript that contains the upstream exon and the reporter/selectable marker.
...
Eighteen transposition events were obtained from distinct cell colonies. Blasting the human genome in the NCBI and ENSEMBL database... indicated that seventeen of them landed in an intron and one of them integrated in an exon at active genomic loci. These data are in consistence with the fact that exons and introns comprise 1.5% and 24% of human genome, respectively.

See here for further reading.